# Internal Kelvin Waves in a Broad, Mid-Latitude Fjord

Sebastien Donnet, Pascal Lazure, A.W. Ratsimandresy, G. Han

► To cite this version:

Sebastien Donnet, Pascal Lazure, A.W. Ratsimandresy, G. Han. Internal Kelvin Waves in a Broad, Mid-Latitude Fjord. Journal of Geophysical Research. Oceans, 2025, 130 (7), e2024JC021664 (30p.). 10.1029/2024JC021664. [hal-05206203](https://hal.science/hal-05206203v1)

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Distributed under a Creative Commons Attribution 4.0 International License
# JGR Oceans

## RESEARCH ARTICLE

10.1029/2024JC021664

**Key Points:**

* Large sub-inertial baroclinic motions are observed in broad, mid-latitude, sub-arctic fjord

* These motions are reproduced by a numerical model; confirming the existence of coastal trapped waves of baroclinic Kelvin nature

* These waves are generated locally and remotely from an "upstream" neighboring embayment and can interact locally in a very non-linear way

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

S. Donnet, sebastien.donnet@lecnam.net

**Citation:**

Donnet, S., Lazure, P., Ratsimandresy, A. W., & Han, G. (2025). Internal Kelvin waves in a broad, mid-latitude fjord. *Journal of Geophysical Research: Oceans*, 130, e2024JC021664. https://doi.org/10.1029/2024JC021664

Received 30 JUL 2024
Accepted 9 JUL 2025

**Author Contributions:**

**Conceptualization:** S. Donnet

**Data curation:** S. Donnet

**Formal analysis:** S. Donnet

**Funding acquisition:** S. Donnet, A. W. Ratsimandresy

**Investigation:** S. Donnet, P. Lazure

**Methodology:** S. Donnet, P. Lazure, A. W. Ratsimandresy, G. Han

**Project administration:** S. Donnet

**Resources:** P. Lazure, A. W. Ratsimandresy

**Software:** S. Donnet, P. Lazure

**Supervision:** P. Lazure, G. Han

**Validation:** S. Donnet, P. Lazure, A. W. Ratsimandresy, G. Han

**Visualization:** S. Donnet

**Writing – original draft:** S. Donnet

© 2025. The Author(s). This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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# Internal Kelvin Waves in a Broad, Mid-Latitude Fjord

S. Donnet¹,² ID, P. Lazure³ ID, A. W. Ratsimandresy⁴ ID, and G. Han⁵ ID

¹Conservatoire National des Arts et Métiers, Institut National des Sciences et Techniques de la Mer (CNAM-INTECHMER), Cherbourg-en-Cotentin, France, ²Laboratoire Universitaire des Sciences Appliquées de Cherbourg (LUSAC), Cherbourg-en-Cotentin, France, ³Ifremer, Laboratoire d'Océanographie Physique et Spatiale (LOPS), Plouzané, France, ⁴Fisheries and Oceans Canada, Northwest Atlantic Fisheries Centre, St. John's, NL, Canada, ⁵Fisheries and Oceans Canada, Institute of Ocean Sciences, Sidney, BC, Canada

**Abstract** Broad embayment, such as some Fjords, can host the generation and propagation of internal Kelvin waves should the ratio of their Rossby radius to shelf-slope width be large. Here, we report on such a process in a broad, mid-latitude, fjord where the upper-layer dynamics are dominated by sub-inertial baroclinic motions. This fjord is of particular interest due to recent development of the aquaculture industry and to being historical fishing grounds. Using a fully non-linear, three-dimensional primitive equation numerical model we show that the large majority of the thermocline vertical fluctuations (80%) and much of the along-shore currents (50%) can be reproduced with a flat-bottom assumption. We use the model to determine the origin of the process, which is expressed by upwelling and downwelling disturbances traveling cyclonically around the bay. We find that the wind generates local and remote, from a large and deep neighboring bay, responses which travel as forced and freely propagating long, coastally trapped, internal waves into and around the fjord. The resulting dynamics within the fjord can therefore be complex, particularly in the fall season during which nearly continuous and directionally variable winds occur. Under such forcing conditions and given the irregularity of the regional coastline, signals combine to form temporally and spatially varying responses, enhancing or diminishing transient upwelling or downwelling and their associated along-shore current pulses.

**Plain Language Summary** Coastal upwelling (cold, deep water brought-up to the surface) and downwelling (warm, surface water brought-down to depth) are typically not static. It is particularly true in places where wind patterns change rapidly and often and where waters are stratified seasonally, such as on the Eastern Canadian coasts. In such places, local upwelling and downwelling disturbances can travel along the coast in such a way as to be felt hundreds of kilometers from their place of origin. This paper is concerned with such phenomena, using a comprehensive set of in situ observations as well as the results from numerical modeling simulations. The study site is a broad and deep fjord, located along the shores of the island of Newfoundland (Canada). We show that remotely generated upwelling and downwelling can interact with locally generated ones in such ways as to amplify or decrease the local conditions within the fjord. These findings should help in managing the development of the aquaculture industry in this region as well as to inform more broadly on the physical processes responsible for such phenomena.

## 1. Introduction

In a stratified and broad embayment, broad defined here as by being wide with respect to its internal Rossby radius, interesting dynamics can take place. Each side of the bay can behave independently, for example a side can be subject to an upwelling while the other is subject to a downwelling, and a wave motion generated (by upwelling or downwelling forcing and/or relaxation) can propagate around as a "trapped" motion with the coast to its right (Northern hemisphere). Should the bathymetric slopes along the coast be steep enough, those motions behave as internal Kelvin waves (iKWs), an asymptotic and simpler form of the more general motion of "coastal trapped waves" (CTWs, Gill & Clarke, 1974) which are modified by both stratification and topography. In essence, CTWs are an hybrid of Kelvin and Continental Shelf Waves (CSWs) which are long waves propagating on shelf-slope region in a homogeneous fluid. A useful parameter that can be used to predict which type of motion is likely to take place is the Stratification parameter S, or Burger number (Burger, 1958):

$$S = \frac{N^2 H^2}{f^2 L^2}$$
Writing – review & editing: P. Lazure,
A. W. Ratsimandresy, G. Han

where *N* is the buoyancy frequency representative of the stratification (rad/s), *H* is the embayment/ocean depth (m), *f* is the Coriolis parameter (rad/s) and *L* is the cross-shore length of the shelf-slope region (m). This number is, hence, dimensionless and a representation of the importance of the internal Rossby radius (*NH/f*) over the shelf-slope width scale *L*. If *S* << 1, the motion is mostly barotropic and takes the form of a CSW and if *S* >> 1 the motion is mostly baroclinic, taking the form of an iKW (Huthnance, 1978).

Evidence of coastally trapped iKWs have been reported in many parts of the world: in large lakes (e.g., Csanady & Scott, 1974; Lemmin et al., 2005; Mortimer, 1968; Saggio & Imberger, 1998), in wide straits (e.g., Proehl & Ratray, 1984), in the Gulf of Mexico (e.g., Hallock et al., 2009), Peruvian Coast (e.g., Romea & Smith, 1983), Japan (e.g., Kitade et al., 1998; Masunaga et al., 2017), India (Shah et al., 2019), Caspian Sea (e.g., Weber & Ghaffari, 2014) in the Mediterranean sea (e.g., de Ruggiero et al., 2018; Vilibić & Orlić, 1999), on the western European shelf (e.g., Batifoulier et al., 2012), in the Baltic Sea (e.g., Fennel et al., 2010; Walin, 1972), Svalbard (e.g., Støylen & Fer, 2014; Svendsen et al., 2002), along the Arctic ocean/Beaufort Sea (e.g., Carmack & Kulikov, 1998) and in Antarctica (e.g., Albrecht et al., 2006). Their widespread geographical representation owes to the basic set of physical characteristics necessary to their existence: stratification, coastal boundary and steep slope (also commonly called coastal wave guide). In many cases, however, the effect of bathymetry is not negligible and the response takes the more complex form of CTWs (e.g., along the US west coast, Southwest Australia coast, Southeastern Africa coast and Southeastern America coast, western European shelf, Caspian Sea and Black Sea).

Since iKWs can transmit upwelling and downwelling conditions away from their generation area, they are a very important process to consider when studying coastal ecosystems and human interactions with them. While confined to a narrow band near the coast (internal Rossby radius scale; few kilometers to few tens of kilometers, typically) and representing less than 1% of the global ocean surface, upwelling regions sustain about a quarter of the world fisheries (FAO, 2020). Marine aquaculture, a fast growing resource of seafood, is also largely located within few kilometers from the coast and thus potentially subject to upwelling-downwelling conditions. iKWs are also a key player with respect to earth climate. Equatorial iKW, for instance, is an important process regulating the ENSO (e.g., Wang, 2002; Wang & Picaut, 2004). iKWs have also been shown to be an important mechanism of heat transport in Arctic fjords which can lead to accelerated rate of glacial melting (e.g., Fraser et al., 2018; Jackson et al., 2018).

The Newfoundland shelf is characterized by a strong seasonal stratification (see Cyr et al., 2024 for the most recent update) and its rugged coastline presents large and deep bays (Figure 1). The shelf is also dominated by a cold and relatively fresh, equatorward current with Arctic origin; wrapping the island with its inner branch (see Smith et al., 1937; Loder et al., 1998; Ma et al., 2016 and references therein). Occurrences of iKWs have been documented on the north coast of Newfoundland by Yao (1986), de Young et al. (1993), and Davidson et al. (2001) but have not been investigated on the south coast where the main ocean dynamics are still poorly known. Fortune Bay is one of those large bays located on the south coast of the island. It is about 130 km long, 20 km wide and has the peculiarity of having its mouth quasi closed due to the presence of the Saint-Pierre and Miquelon (SPM) archipelago at its SW boundary but to be semi-opened on its western boundary which consists of a series of islands and shallow sills; 76 m mean and 125 m max depth from Miquelon to Brunette island and 53 m mean and 108 m max from Brunette to the main land (see Donnet, Cross, et al., 2018 for details and Figure 1). Fortune Bay is deep, reaching more than 400 m in its main basin, oriented SW-NE, and about 600 m in its prominent head, Belle Bay, oriented SE-NW. Hence, its sides are steep and while the maximum cross-shore width of the shelf-slope region reaches about 15 km in the outer part, it is generally well below 5 km (see Figure 1, using the 200 m contour as representative of the bottom of the slope). In Belle Bay, *L* is very small and can be close to 0 km (i.e., a vertical wall). In a recent oceanographic review of the area, the internal Rossby radius was estimated to range between 5 and 10 km from spring to fall using a monthly hydrographic climatology and a 2-layer approximation (chapter 2). Same order is found in this study using a normal modes approach (details below). Thus, the stratification parameter of Fortune Bay is generally larger than 1 and iKW dynamics can be expected.

A first set of oceanographic investigations took place from the 1980s to early 1990s in Fortune Bay, with a focus on deep water renewals (de Young & Hay, 1987; Hay & de Young, 1989; White & Hay, 1994). In the early 2000s, further studies were undertaken following a rapid development of the aquaculture industry (Newfoundland south coast in general and Belle Bay in particular) which led to a geographic and hydrographic description of the area (Donnet, Cross, et al., 2018; Donnet, Ratsimandresy, et al., 2018) as well as ocean currents and water exchange
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Study area. Dots represent oceanographic mooring observation sites (water column temperature and ocean currents data) and triangles represent weather stations (wind data). In red are the primary sites used in this study (F3B01-08 moorings and SAGIS weather station), in orange are the secondary sites used for complementary information (F3B09-10 moorings and DOGIS weather station) and in yellow are cited sites not used herein due to period coverage differing from that studied (F3B11&12). Bathymetric contour represented in bold is that of the 200 m isobath, corresponding to the bottom of the continental slope of Fortune Bay. Other isobaths represented by thin black lines are from 50 to 250 m; spaced every 50 m.</figcaption></figure>

studies (Ratsimandresy et al., 2019, 2020). Following those latter works, an oceanographic study, focused on Fortune Bay, was launched in 2015 to investigate the main physical processes affecting the upper layers of the fjord and their forcing mechanisms. An important motivation to this work, aside from the aquaculture development, was the results of a first effort looking at the ocean response of Belle Bay to strong wind (Salcedo-Castro & Ratsimandresy, 2013) as well as of the results of earlier studies done in other large bays mentioned above. The works of Yao (1986) and de Young et al. (1993), in particular, largely influenced the sampling design and main hypothesis of this new study. On the other hand, while Salcedo-Castro and Ratsimandresy (2013) described important bay scale responses to strong winds (barotropic and baroclinic) they could not determine their nature nor geographical origin(s) from the data available at the time, which was an added motivation to investigate these aspects.

A first paper presents the result of these recent observations and illustrates the presence of upwelling and downwelling disturbances traveling within the bay (Donnet et al., 2020). A second paper describes this process and associated currents in more details; showing a cyclonic propagation and bay-scale correlation of the isotherms and along-shore variations (Donnet et al., 2022). The objectives of this third paper are to:

* Determine the nature of the dominant physical process responsible for the strong current pulses described earlier, with respect to an iKW hypothesis, in particular.

* Determine the origin of this process (forcing and spatial location) including local versus remote effects.

* Describe the characteristics of the signal propagation within the fjord.
An emphasis on numerical modeling will be given in this study to provide with a more detailed view of the process in time and space, including its physical dimension (along and across shore), its propagation and fate within the bay (potential modification and exit) while observations will be used to both validate the numerical model simulations and better assess the nature and characteristics of the main process studied. In turn, the results of these numerical simulations could be used in future studies to predict the transport of variables of interest such as virus, sea-lice or organic material originating from aquaculture farms or larvae from species of economical interest (e.g., local fisheries).

This paper is organized as follow: a first section describes the observations and numerical model used (Material and Methods), a second section presents the results starting with a description of the observations, followed by a validation of the model and finishing with idealized runs allowing us to identify and describe the main process involved (Results), a third section discusses the results in light of the objective stated above (Discussion) and a fourth section concludes our findings and provides some perspectives (Conclusion).

## 2. Materials and Methods

### 2.1. Observations

The majority of the data used for this study were collected during an observation program that spanned May 2015–2017 and that focused on the collection of continuous temperature and ocean currents profiles. 12 sites were monitored in total, for 6 (F3B09-12), 12 (F3B05-08) and 24 (F3B01-04) months (see sites location in Figure 1). Temperature profiles were collected for nearly all the water column (5–10 m depth to 5–10 m above sea bottom) while current profiles spanned either about the same or just over half the water column for the most part (i.e., from 80 m up). All the moorings but two (F3B08 & F3B12) were deployed on the slope: F3B01-04 in 150–160 m depth and F3B05-07&11 in 90 m. F3B08 was deployed at the bottom of a nearly vertical slope in 210 m depth and F3B12 was deployed in a river mouth in 10 m depth. Details of this monitoring program, limitations and data return are presented in Donnet et al. (2020). For this study, F3B01-08 data collected during the stratified period of year 2 (May–November 2016) are used to validate the numerical model simulations and to help determining the nature and propagation characteristics of the processes investigated. Note that, on a cyclonic sense (which will be shown to be the propagating sense of the main signals) the moorings sequence is: F3B01, 05, 08, 04, 07, 03, 06, and 02. Wind data collected during this program (DOGIS, Figure 1) are also used to illustrate the spatial variability of this parameter.

These data are complemented by wind speed and direction timeseries from Environment and Climate Change Canada (ECCC) Sagona Island weather station (SAGIS in Figure 1) which are used as our primary wind data for our analyses and numerical simulations and by a temperature and salinity monthly climatology presented in Donnet et al. (2022) which are used to initialize the model.

In addition, spatial wind and Sea Surface Temperature (SST) fields are used to illustrate the atmospheric forcing and ocean surface response during selected events (for model setup and validation). Wind data came from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis (~25 km horizontal resolution, hourly fields, Hersbach et al., 2018) and ECCC high resolution model High Resolution Deterministic Prediction System (HRDPS, ~2.5 km horizontal resolution, hourly fields, ECCC, 2022). SST came from 3 different data set (the 4 km resolution, daily, AVHRR Pathfinder v5.3 re-analysis (PFv5.3, Saha et al., 2018)), the 1 km resolution, daily, Global Foundation SST analysis (Chao et al., 2009; G1SST, JPL, 2010) and the 1 km resolution, daily, MUR Global Foundation SST analysis v4.1 (Chin et al., 2017; MURSST, JPL, 2015).

### 2.2. Numerical Model (FVCOM)

We used the Finite Volume Community Ocean Model (formerly known as Finite Volume Coastal Ocean Model, FVCOM, Chen et al., 2003, 2013). FVCOM is a fully non-linear, free-surface, three-dimensional hydrodynamic model solving the primitive equations (Navier-Stokes) on an unstructured computational grid (mesh) in the horizontal and on terrain-following coordinates in the vertical. FVCOM uses the finite volume method to solve the governing equations in an integrated form and invokes the time-splitting method separating the barotropic and baroclinic modes to increase computation efficiency. We used FVCOM v4.1 in prognostic mode (i.e., time-varying density fields) and under the hydrostatic approximation. The latter being justified by an expected large horizontal scale of the process studied compared to its vertical scale (kilometers vs. tens of meters). Given
the latitudinal scale of the study area (order of 100 km) we also choose to use the *f*-plane approximation (i.e., constant Coriolis parameter) and Cartesian horizontal coordinates (Universal Transverse Mercator, UTM). Although we investigated the potential effect of the bathymetry (details in the discussion) we use a flat-bottom approximation for all the simulations presented herein to isolate the iKW dynamics.

The mesh was created using the Aquaveo Surface-water Modeling System software (SMS v13, Community Version) and following the constraints recommended by FVCOM users' manual (Chen et al., 2013, Chapter 20). The coastline data came from the Global Self-consistent, Hierarchical, High-resolution Geography Database (GSHHS v2.3.5, Wessel & Smith, 1996, 2018) providing an original resolution of about 100 m. Using SMS resampling tool, and considering an internal Rossby radius on the order of 5–10 km, a minimum horizontal resolution of 1 km was selected within the area of interest (i.e., Fortune Bay) to ensure proper representation of the expected cross-shore dynamics (upwelling & downwelling, in particular). The SPM archipelago was resampled at 1.5 km (Saint-Pierre) to 2.5 km (Miquelon) while the rest of the coastline was resampled at 5 km and was very much simplified (removal of many islands and small inlets). The open-boundary (shelf area) was resampled at 10 km. Early simulations with a minimum of 5 km resolution in Fortune Bay were attempted and succeeded in reproducing the main dynamics observed, that is upwelling and downwelling events, but the cross-shore scale of the processes did not appear optimum. Much higher resolutions were tested when using a realistic bathymetry, down to a 100 m value, which will be discussed later. Given the relatively small domain, relative low resolution, use of an unstructured grid and computing power available, a conservative external time step of 1 s (with a mode ratio of 10) was used all along and for all the mesh resolutions without falling under the Courant-Friedrichs-Levy (CFL) criterion/condition (about 80 m minimum cell size for a maximum depth of 600 m). Two flat bottom mesh were created at 1 km resolution: a “local” mesh, centered on Fortune Bay and an “extended” mesh including the neighboring Placentia Bay to test the hypothesis of potential remote effects from this other large bay on Fortune Bay. These effects were further assessed using idealized wind scenarios in which wind was applied on restricted areas of the extended mesh; that is, applying the stress on Fortune Bay area and on Placentia Bay (Figure 2).

Three vertical coordinates systems are available with FVCOM: uniform, geometric and generalized. The uniform system distributes the levels evenly with depth, the geometric system increases resolution near the surface and near the bottom to improve calculation of the Ekman layers dynamic and the generalized system leaves the user to define spacing in the upper and lower layers down to a, also user defined, depth. Upon a number of trials, we found that a generalized coordinates system was the most appropriate with flat bottom simulations and that 20 (using a 150 m bottom) to 40 (using a 300 m bottom) layers were sufficient to reproduce the vertical density profile and its evolution when comparing with the observations. We used a vertical resolution of 5 m for the first 50 m (10 layers) and 10 m for the last 50 m (5 layers) leading to a resolution of 8–10 m for the rest of the water column. Sensitivity of the model with depth was gauged by running all the simulations used for validation with 150 and 300 m depth, roughly corresponding to mid and bottom slope at most observation sites, respectively. While 150 and 300 m simulations led to nearly equivalent results, the 300 m ones were slightly better correlated with the observations (with currents, in particular) and were so retained for all the results presented herein.

The initial conditions of temperature and salinity were taken from the spatially homogeneous monthly clima-tology presented in Donnet et al. (2022). Data covering Fortune Bay as a whole were used to create a “summer” profile (i.e., an average of July, August and September profiles) for the July 2016 events simulations and to create an August profile for the September 2016 events simulations (the 2 main scenarios selected for this study). Those profiles were found to correspond best with the observations available for these periods (see Figure S1 in Sup-porting Information S1).

Winds from ECCC SAGIS weather station were used as surface boundary conditions and assumed horizontally homogeneous. Since SAGIS is located on a small barren island roughly in the middle of the domain, it was considered to be representative of the wind field of the area. This assumption is justified here also by the limited study area which is much smaller than the synoptic scale (i.e., weather systems). The validity of this assumption was tested by plotting spatial wind fields from the ECMWF ERA5 re-analysis and ECCC's HRDPS model data (see Figure S2 in Supporting Information S1 and hourly snapshots provided in Donnet and Lazure (2023)). Both sources show a largely homogenous spatial field over our area of interest, especially during strong wind events (e.g., July 4–5) and they both compare very well with SAGIS observations (Figure S3 in Supporting Informa-tion S1). SAGIS winds are available hourly and were gap-interpolated when and where necessary (3 hr maximum gap found for the periods simulated). Input wind speed is converted by FVCOM to wind stress using the Large
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Meshes used for the numerical simulations. “Local” and “Extended” meshes represented here use a flat bottom approximation. Observation points (mooring sites) used for validation are represented by black squares and are located 2 elements or nodes away from the coast (i.e., about 2 km away). Elements used for ideal wind forcing local (“FB only”) versus remote (“PB only”) scenarios are represented in blue and red, respectively.</figcaption></figure>
and Pond (1981) relationship. On the offshore boundary, and while data from the Saint-Pierre tide gauge (SHOM, 2022) were used for model testing and validation purposes (e.g., barotropic tides simulations) the water level was “clamped” to zero for all the simulations presented herein (i.e., no sea-level variation allowed along the offshore open boundary). Tides have very little influence on the currents in the region (Donnet et al., 2022; Ratsimandresy et al., 2019) and we wanted to focus the analysis on the response to wind forcing. Clamping the offshore boundary can have undesirable effects, however, such as limiting the generation of a signal near the southeastern boundary, that is bottom on the Burin Peninsula, for instance in the case of the generation of an upwelling or downwelling. A sponge layer of 15 km (1–2 elements) was prescribed along the offshore boundary and the “no gradient” condition was used for all simulations. A small “ramp-up” time of 9,000 time-steps (i.e. 9,000 s or 2.5 hr) was also applied on the forcing series to minimize spurious responses. No surface heat or precipitation-evaporation fluxes, no groundwater fluxes, no atmospheric pressure, no river input, and no open ocean conditions were stipulated; reducing the forcing to a wind-only one applied to the computational domain.

We used Mellor and Yamada (1982) level 2.5 (MY-2.5) vertical turbulent closure sub-model with a background vertical mixing coefficient of $1 \times 10^{-5} \text{ m}^2/\text{s}$ for all simulations presented herein. Sensitivity tests, varying this coefficient by a factor of 10, did not show any significant effect on the results. For horizontal mixing, we used a constant coefficient of $0.3 \text{ m}^2/\text{s}$. Using a constant coefficient within a range of 0–$0.3 \text{ m}^2/\text{s}$ had very little effect on the flat bottom simulations. However, using the available Smagorinsky parametrization (Smagorinsky, 1963) would increase horizontal spreading and lower currents strength well below that observed. Both horizontal and vertical Prandtl numbers were set to 0.1 and is defined in FVCOM as the ratio of thermal eddy diffusivity to eddy viscosity, so the inverse of its more common definition in fluid mechanics. A logarithmic bottom layer is used in FVCOM and a roughness height of 0.001 m and maximum drag coefficient of 0.0025 were chosen.

# 3. Results

## 3.1. Observations

Figure 3 illustrates the strong seasonality in stratification experienced in the region, peaking in August with SST about 16°C and salinity mostly below 31 g/kg lying above waters less than 2°C and more than 32 g/kg in salinity. Although individual profile taken at any given time can show a surface mixed layer these monthly climate results are smooth, and density profiles show a continuous stratification from spring (May) to fall (November). In summer, this continuous stratification occurs in the first 30–40 m while it is somewhat shallower in spring (about 20 m) and much deeper in fall (about 80 m). Differences of density of $1 \text{ kg/m}^3$ (spring) to $3 \text{ kg/m}^3$ (summer) are found between the surface and sub-surface layer (which is an intermediate layer, in the case of Fortune Bay; see Donnet et al., 2022 for details) and the buoyancy frequency peaks around 0.03 rad/s in summer corresponding to a natural oscillation period of about 3 min. In spring and fall, peak values of N are on the order of 0.01 rad/s (about 10 min natural periods).

Using these seasonal profiles and performing a normal mode analysis (Klinck, 1999; see Figure 3 and Figure S5 in Supporting Information S1 for illustrations) yields to mode 1 internal wave phase velocities of 0.4 m/s in spring (May) to 0.7 m/s in fall (November) in water depth $H = 300 \text{ m}$. Summer conditions used for the modeling simulations (details below) lead to a mode 1 phase speed of 0.6 m/s with an inversion around 50 m (August profile; September events scenario) to 65 m (Jul–Sep averaged profile used to reproduce the July events and for the idealized scenarios; Figure 3) in $H = 300 \text{ m}$. Mode 2 and 3 velocities are about half and third of mode 1 values, respectively. At the latitude of Fortune Bay (47.5°N), this leads to a mode 1 internal Rossby radius of about 4–7 km from spring to fall (using $f = 1 \times 10^{-4} \text{ rad/s}$) with a value of 6 km for the modeling scenarios considered herein.

Timeseries of wind and thermocline depth during the most stratified period of the year (from May–November 2016) are illustrated in Figure 4. Two weather stations series are represented, that of DOGIS, located in the middle of Belle Bay, and that of SAGIS, located more offshore (Figure 1); overall, the two series are consistent with each-other although winds from the North are generally stronger at DOGIS while winds from the west and southwest are generally stronger at SAGIS. Thermocline depth is presented using the 2°C isotherm which roughly corresponds to the bottom of the surface stratification (Figure 3). Wind forcing is characterized by intense but relatively short-lived peaks of 5–10 m/s speed (or more) and, typically, 2–4 days (d) in duration (“trough to trough”). Those strong events can occur from just about any direction but with a predominance of winds from the Northwest (NW) and from the Southwest (SW). Few strong events from the Northeast (NE) and Southeast (SE)
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Water stratification profiles (top 4 panels). Seasons are represented by their “peak” month (FEBruary for winter, MAY for spring, AUGust for summer and NOVember for fall). Bottom panel illustrates the vertical structure of freely propagating waves horizontal currents (first 3 vertical modes) calculated from on an averaged Jul–Sep hydrographic profile (using Klinck, 1999).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Wind speed and thermocline depth timeseries (6 hr moving-averaged). Wind direction (from) is indicated on top of main events (N for North, NW for NorthWest, etc.). Thermocline depth is illustrated via the depth of the 2°C isotherm, the flat lines toward the end of the series indicate a depth of the isotherm larger than the deepest sensor located on the mooring, affecting F3B05, 06, 07, and 08 (about 80 m limiting depth). Timeseries are grouped in two shores corresponding to main cardinal directions. Non-shaded in gray are the periods selected for analyses and numerical modeling.</figcaption></figure>

are notable though, such as the one of mid-July (NE-NW event). The frequency and intensity of the events visibly increase during the fall.

In this paper, oceanic motions will be described as “events” and “pulses” which are defined as follows: an event is a perturbation consisting of a descending (downwelling) and an ascending (upwelling) phase of the isotherms. A pulse is defined as unidirectional currents (inflow or outflow) generally associated to a phase (either downwelling or upwelling). Thus, a downwelling event is a period generally starting with a downwelling pulse and, generally, finishing with an upwelling pulse; conversely, an upwelling event starts with an upwelling pulse and finish with a downwelling pulse. Atmospheric forcing events usage differs a little in a sense that an event is defined as a sustained period of wind going in the same direction using the four main quadrants listed above. Along-shore and across-shore components will also be used, for both wind forcing and oceanic responses, using Fortune Bay's main axis orientation as a reference, that is 40° from the north, for the wind and using site specific isobaths orientation for the ocean currents.

Thermocline depth measured around the bay shows important upwelling and, even larger, downwelling (Figure 4). Those events appear transient until late summer (September) when they start to be more frequent to the point of appearing periodic (around 2–5 days). Typical downwelling range is on the order of tens of meters, reaching around 60 m during the largest event in July. Statistical analyses presented in Donnet et al. (2022) showed strong isotherms correlation amongst mooring pairs from F3B08 to F3B06 (anti-clockwise) and the lowest correlation of F3B02 with any other; the latter being visibly distinctive from the other in Figure 4. Donnet et al. (2022) also showed that these upwelling and downwelling events were associated with strong pulses of along-shore current, traveling cyclonically around the bay.

Results of a wavelet analysis (using Grinsted et al., 2004 programs; see Figure S6 in Supporting Information S1 for illustrations) performed on along and across wind speed components of Fortune Bay (40°N orientation for the along component) indicate that strong episodic wind events are generally located within the 1–4 days band (numerous higher frequency events are also apparent but are much less energetic; about 1/4–1/8 in power). 1–2 days events are more frequent in the along-shore component than on the across-shore component. Long, 4–8 days events are only showing up on the along-shore component during the first half of July and second half of September, in particular. Analysis of near-surface (10 m) and sub-surface (70 m) along-shore currents from F3B08 to F3B02 (i.e., excluding F3B01&05, the southeast shore of the bay, due to data limitations) show longer lasting low-frequency pulses
(>1 day period) than the wind. In the near-surface, the period of early July to mid-August and mid-September to mid-October are particularly active with signals located in the 4–8 days band. Within that same band, near-surface events appear to also become more continuous from F3B08 to F3B06. Sub-surface currents are dominated by lower-frequency signals (>4 days periods), particularly at F3B04. A large band, centered on the 16–36 days periods is also visible at all sites. Although not continuous, the semi-diurnal tide band, centered around 0.5 days, is clearly visible at F3B02 (near-surface and sub-surface) and at F3B06 (sub-surface).

Two periods were selected to investigate the process responsible for those upwelling&downwelling events propagating cyclonically: 01–20 July and 04–30 September (Figure 4). The former is an example of transient events, including the largest downwelling event of the timeseries, while the latter is an example of quasi-periodic events. Figure 5 illustrates wind forcing, isotherms variations and associated currents of those events. Wind forcing is represented by the along-shore stress which was calculated using the relationship of Large and Pond (1981) and is positive when going into the bay. Due to data limitation (see Donnet et al., 2020) current speed only (scalar) are represented for F3B01&05 while along-shore currents are shown for the other sites. Along-shore currents are defined as being positive for a flow going into the bay (red color), that is northeast-ward in the outer part and northwest-ward in Belle Bay, and negative (blue color) for an outgoing flow.

In July, four main wind events occurred: a first positive along-shore stress event starting on 3 July followed by a negative stress event ending on 8 July and a second negative along-shore stress event starting on July 10 followed by a positive stress event ending on 17 July. The signal of each couple of events, 3–8 July and 10–17 July, is fairly symmetrical; each event of wind stress (either positive or negative) being of about the same duration, that is just over 2 days for the first couple and just over 3 days for the second one. Each event peak around 0.1–0.15 N/m². At the same time, 2 main downwelling events can be accounted for (dash lines and double-headed arrows): from the 3rd to the 10th and the 12th to the 20th and beyond (across sites). The downwelling phase takes about 2 days to propagate, cyclonically, around the bay the first time and about 4 days the second time (from F3B01 to F3B06). Both downwelling and upwelling phases are associated with an increase in along-shore currents speed but the downwelling phase appear clearly more energetic and logically occupies a much larger proportion of the water column. Downwelling ranges are up to about 20 and 40 m (first and second event, respectively; using the 4°C isotherm as indicator) and each event last about 4 days (first event) to 6 days (second event). Note that prior to the downwelling phase of the second event an upwelling phase also occurred, from the 11th (F3B01, weak) to 16th (F3B06, stronger), that is during negative wind stress forcing (11–13). The duration and timing of the oceanic events appear compatible with the wind forcing, indicating a system locally forced, that is downwelling during positive stress and upwelling during negative stress along the east side of the bay (F3B01&05) with a cyclonic propagation around the bay (from F3B01 to F3B06). However, one can note that the second (and also largest) downwelling event starts 1–2 days prior to the wind stress becoming positive (on July 13th at F3B05 and on July 12th at F3B01) and thus, during a phase of locally upwelling favorable wind (11–13). A downwelling event is also clearly visible between the 8th and 9th at F3B01 and 05 (2°C isotherm) while there were no along-shore wind (i.e., zero stress) and appears to propagate cyclonically (as seen on F3B04-06 with a slight drop of the isotherms and negative along-shore current, associated). The dynamic appears therefore more complex than solely responding to local wind forcing.

In September, three main positive peaks (11–16, 16–19 and 21–24) and 2 negative peaks (19–21, smallest, and 28–30, largest) of along-shore wind stress occurred. Cyclonic propagation of events is again evident but the isotherms and currents picture is more complex. Performing a zero-crossing analysis on the clearest period of the low-pass filtered 4°C isotherm series (September 09–29, 24 hr window running average) yields the identification of 6 (F3B01) to 3 (F3B08 to 06) main downwelling events of 3 (F3B01) to 6 (F3B08 to 06) d duration (or period) with vertical ranges of 13 m (F3B01) to 24 m (F3B04), on average (Figure 5, dash lines and numbers). Hence, the signal seems to change frequency (from high to low) and to be enhanced (in amplitude) as it travels from Fortune Bay's main basin to Belle Bay and out. A "transition zone" can also be noted between F3B08 and F3B04 where, for instance, the near-surface current oscillates between the events 1 & 2. Downwelling associated currents appear, here also, clearly more energetic (order of 0.5 m/s in downwelling vs. 0.25–0.5 m/s in upwelling).

Cross-correlations between mooring pairs F3B01–06, F3B01–08 and F3B08–06 were performed to quantify the relationships and to get an idea of the signals phase propagation speed (Table 1 and Figures S6–S7 in Supporting Information S1 for illustrations). For the September events, the analysis was done on the same time window as the zero-crossing, that is 09–29 September, and using the same isotherm. While correlations with no lag are generally
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Temperature and current speed profiles at mooring sites around Fortune Bay. Along-shore currents (positive into the bay) are represented for F3B08, 04, 03, 06 and 02 while scalar only (modulus) is presented for F3B01 and F3B05 due to data limitations (see Donnet et al., 2020 for details). Downwelling (DW) and upwelling (UW) events are also indicated (using numbers on the September plots). Selected events for the analysis are further indicated by the dash lines (and horizontal double-headed arrows on the July plots).</figcaption></figure>
<table><caption>**Table 1**
Lagged Cross-Correlation Observations Results</caption><thead><tr><th>Mooring pair (km)</th><th>Event</th><th>r (δt = 0)</th><th>r<sub>max</sub> (%var)</th><th>δt (r<sub>max</sub>) (d)</th><th>c (m/s)</th><th>DWdiff (m) (% change)</th></tr></thead><tbody><tr><td>F3B01-06 (180)</td><td>01–10 July</td><td>-0.17 (3%)</td><td>0.82 (67%)</td><td>-1.9</td><td>1.1</td><td>9 (185%)</td></tr><tr><td>F3B01-08 (120)</td><td>01–10 July</td><td>0.65 (42%)</td><td>0.87 (76%)</td><td>-0.8</td><td>1.7</td><td>8 (156%)</td></tr><tr><td>F3B08-06 (60)</td><td>01–10 July</td><td>0.08 (1%)</td><td>0.96 (92%)</td><td>-1.1</td><td>0.6</td><td>1 (11%)</td></tr><tr><td>F3B01-06 (180)</td><td>10–20 July</td><td>-0.50 (26%)</td><td>0.96 (91%)</td><td>-3.8</td><td>0.5</td><td>-4 (20%)</td></tr><tr><td>F3B01-08 (120)</td><td>10–20 July</td><td>0.17 (3%)</td><td>0.92 (85%)</td><td>-2.4</td><td>0.6</td><td>-1 (5%)</td></tr><tr><td>F3B08-06 (60)</td><td>10–20 July</td><td>0.21 (5%)</td><td>0.81 (66%)</td><td>-1.4</td><td>0.5</td><td>-3 (17%)</td></tr><tr><td>F3B01-06 (180)</td><td>09–29 Sep</td><td>-0.31 (9%)</td><td>0.49 (24%)</td><td>-2.2</td><td>0.9</td><td>0 (1%)</td></tr><tr><td>F3B01-08 (120)</td><td>09–29 Sep</td><td>-0.19 (4%)</td><td>0.43 (19%)</td><td>-1.3</td><td>1.0</td><td>5 (45%)</td></tr><tr><td>F3B08-06 (60)</td><td>09–29 Sep</td><td>0.38 (15%)</td><td>0.89 (80%)</td><td>-0.9</td><td>0.8</td><td>-5 (38%)</td></tr></tbody></table>

Note. r is the Pearson correlation coefficient. Lag (δt) is negative when first mooring of the pair is leading the second (e.g., F3B01 leading F3B06). c = phase speed calculated as distance between mooring pair (indicated in bracket) divided by δt. DWdiff = Downwelling amplitude difference between the mooring pair; a positive sign indicates second mooring observed a larger downwelling than the first (e.g. F3B06 downwelling of 01–10 July was larger than F3B01 one by 9 m).

low (<10% of variance), high correlations are found with lags on order 1–4 days (as expected from Figure 5). Higher correlations are found with the July events than with the September events for the pairs F3B01-06 & F3B01-08 while the F3B08-06 pair stayed highly correlated for both periods. As noticed above while describing Figure 5, a remarkable difference in propagation time is found between the first and second event of July increasing from about 2 days in 01–10 July to 4 days in 10–20 July between F3B01 and 06; that is a factor 2 increase. The largest change occurs between the mooring pair F3B01-08 which show a factor 3 increase in lag time from the first to second event (from 0.8 d to 2.4 days). In comparison, mooring pair F3B08-06 show an increase of about 30% only (from 1.1 to 1.4 days). Thus, the second downwelling event of July clearly propagated much more slowly than the first one, particularly between F3B01 and F3B08. Using mooring distance between pairs leads to estimates of phase speed of the order of 0.5 m/s (second event for all pairs and first event between F3B08-06) to 1 m/s (first event between F3B01-08) in July and about 1 m/s in September (all mooring pairs). There are uncertainties with these latter estimates, however, due to the complex coastline which made the computation of distances difficult. We assumed, notably, that the signal would travel back and forward within both Terrenceville inlet (about 15 km long) and in the head of Belle Bay (F3B12; about 10 km long) even though their cross-sections are about 3 km; that is, smaller than the internal Rossby radius (estimated at 6 km earlier). Model results presented below show, however, that the signals do propagate within these narrow features (in and out) although they appear to be partially reflected as well; consistent with previous studies on propagation of iKW in narrow straits and fjords such as Durland and Qiu (2003) and Jackson et al. (2018). Another remarkable result is on the change of signal amplitude which significantly increased along the bay during the first event of July (by 185% from F3B01 to F3B06) while decreasing slightly during the second event (by about 20% from F3B01 to F3B06, Table 1). Most of the amplitude enhancement of the first event occurred between moorings 01 and 08, in contrast to the modest reduction observed between moorings 08 and 06 during the second event. On the other hand, the events of September show little changes in both signal phase speed and amplitude from F3B01 to F3B08. It should be noted, however, that other than for the F3B08-06 pair, the correlations are not high for this period (0.4–0.5); reflecting the important change in signal frequency (from F3B01 to F3B06) noted above.

Considering the events' duration and phase speed determined above, wavelengths can be estimated. Hence, for a phase speed ranging from 0.5 to 1 m/s (second and first event, respectively) and event duration ranging from 4 to 6 days (first and second event, respectively) we obtain wavelengths of the order of 260 km (second event) to 350 km (first event). In September, this range increases from 260 km (3 days event duration) to 520 km (6 days event duration) using a constant phase speed of 1 m/s. Given the uncertainties associated to the determination of the phase speed and events duration noted above, there are inherent uncertainties with those estimates. Nevertheless, they provide with a first order, 2–3 times the bay's length, which will be refined using the results of the numerical model.
Downwelling and upwelling is expected on the eastern shore (F3B01&05) during positive and negative along-shore wind stress, respectively. These disturbances are also expected to propagate cyclonically around the bay as iKWs should the cross-shore scale, that is bay width, allows them to do so (Jackson et al., 2018); a valid expectation in Fortune Bay which is 20 km wide for an internal Rossby radius less than 10 km. As mentioned above, partial reflection is also expected in some of the small inlets surrounding the bay. Though positive along-shore wind stress and downwelling events appear correlated, particularly during the July events, it is, however, more difficult to discern the effect of negative along-shore stress (both in July and in September) and to untangle the apparent change of frequency between the main basin (F3B01&05) and the head of the fjord (F3B08, 04 & 03) during the September events. Assessing the nature of the process responsible for the propagation of those events as well as its forcing mechanisms more definitively (i.e., positive vs. negative stress) will be the focus of the following section using the numerical model. Suspected remote effect(s) and a further assessment of signal propagation will also be given using the results of this tool.

## 3.2. Numerical Model Validation

Figure 6 shows the thermal and currents structure evolution in time of July (A) and September (B) events as observed and as modeled (flat bottom local and extended mesh runs). Only F3B01 and F3B06 are shown for conciseness and for being representative of “upstream” and “downstream” conditions (i.e., of signals propagating cyclonically as seen in Figure 5). More complete comparisons using the 4°C isotherm depth and along-shore currents between the observation and model results, which were used for quantification, are shown in the (Figures S8–S11 in Supporting Information S1). We selected the 4°C isotherm as representative of the thermocline depth and as a good marker between the surface and lower layers. Along-shore currents were calculated as a depth average from the surface to the 4°C isotherm depth, therefore representing a depth varying surface layer. Nodes and elements used for the comparisons were taken about 2 km from the coast to be as representative as possible considering a flat bottom approximation and average across-shore distance from moorings of about 2 km (0.5–7.5 km range).

In July (Figure 6a), the largest differences between the model runs and observations occur at F3B01. The local model overshoots the first downwelling event (4 July) but underestimates the second one (14–16 July) significantly. The local model is also late by about 1 day for this second event and misses the downwelling event of July 9th (observed by the 2°C isotherm). While the extended model also overshoots the first event, it does a much better job at reproducing the second event being both in phase with the observation (14–16 July) and about the right magnitude with the 4°C isotherm. The 2°C isotherm downward migration is, however, lesser with the extended model than observed and rebound of both the 2 and 4°C are slower (taking about 3 days to go back to pre-event depths instead of about 2 in the observations). A downwelling event is also represented on July 9th by the extended model (unlike the local model) but last longer than the observations and affect a larger part of the water column as indicated by the 4°C isotherm. At F3B06, both models reproduce the observations reasonably well (in amplitude and phase). Interestingly, the extended model does not reproduce the second, and largest, downwelling occurring on the 17th (i.e., 3 days after F3B01) any better than the local model this time. This is in fact the case from the site F3B08 and all-around Belle Bay (F3B04, 07 and 03; see Figures S8 and S9 in Supporting Information S1). The observed downwelling of July 12th is also represented by both models.

High frequency variability (<1 day) are present in both models for which spectral analyses (not shown) indicate as being from near-inertial (~17 hr) band origins. Spectral analyses made on the observations indicate semi-diurnal signals of likely tidal origin (at F3B02, in particular) but do not reveal any near-inertial peaks (see Donnet et al., 2022 for more details). Since the models were run without tidal forcing; we suspect the model signals to be the result of Poincaré waves propagating in the domain. Modeled near-inertial and observed semi-diurnal signals are on the order of few meters (5 m at most) in isotherm amplitudes and of the order of few cm/s (0.05 m/s at most) in currents speed. These signals are most prominent at F3B02, about half the amplitude at F3B01, 05 and 06 and hardly visible anywhere in Belle Bay in both model and observations results. They are small signals, however, compared with the downwelling and upwelling events and will therefore not be considered any further in this study.

In September (Figure 6b), both models reproduce the observations better at F3B06 than at F3B01. At F3B01, the first modeled downwelling event (5–7 September) is too small and the large downwelling events observed by the 2°C isotherm from the 11th to the period's end are not as distinct in the models. The quasi-absence of the first
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Model validation using July events (a) and September events (b). Observed current speed scalar only are represented at F3B01 due to data limitations (Donnet et al., 2020). Observed along-shore currents are represented otherwise at F3B06 and at both sites with the models. Along-shore is positive for a flow going into the bay (red color) and negative (blue color) for an outgoing flow.</figcaption></figure>
event might be explained by model spin-up time, however, and by the fact that this event may have originated from a previous wind event, not included in the forcing timeseries. The difference in variability of the 2°C isotherm, on the other hand, may be, in part, explained by the difference of that isotherm depth between the initial conditions and the observations (about 40 vs. 60 m, respectively) and/or the results of other processes not taken into consideration by the models. Although smaller, some of the variability is captured nonetheless and some difference between the local and extended models can be noted. The extended model does not overshoot the event of the 10th to 11th as does the local model and captures the large event of the 20–23 better than the local model (although late by about 1 day). Both models miss the notable downwelling event centered on the 26th, however. At F3B06, the first event (7–11) is also largely underestimated by both models, as we could expect, but the next three (14–16, 19–21 and 23–25) are reasonably reproduced. The last downwelling event (28–29) is largely missed by both models. The upper layer currents are reasonably well reproduced by the models at F3B06 and in fact from F3B08 to F3B06 (Figures S10 and S11 in Supporting Information S1) but the modeled lower layer currents appear weaker. The choice of the bottom depth influences this, and the 150 m simulations provided slightly better results for that layer at that site. It should be noted that current inversion, occurring around 40–50 m during some events (14–16 and 19–21, in particular) do not systematically occur as the model would suggest.

SST data were analyzed as means of validation during upwelling events, which are expected to be manifested by bands of colder water near the coast. To make the results comparable, hourly model output was daily averaged. Unfortunately, examination of daily snapshot derived from three different data set (PFv5.3, G1SST and MURSST, described above) proved to be inconclusive (see Figure S12 in Supporting Information S1 as well as complete snapshot series in Donnet and Lazure (2023)). Upwelling events indicated by the moorings in 8–10 July (from F3B05 to F3B06) or 13–15 July (F3B04-06), for instance, do not appear clearly in any of the data set. PFv5.3 lacks coverage for both periods and the signals are either not clear (8–10 July) or absent (13–15 July) from the other data set. The model, on the other hand, shows clear upwelling signatures all along the Burin Peninsula and northern coast of Belle Bay. The following aspects may explain this apparent discrepancy: 1/cloud coverage is severe in this region which affects PFv5.3 AVHHR data particularly (Donnet et al., 2022) but also likely affects blended analyses such as G1SST and MURSST, 2/the blending and interpolation used in G1SST and MURSST, albeit necessary to provide gap-free coverage, may significantly smooth our signals that are largely contained within a thin band near the coast (~5 km), 3/the (also necessary) daily averaging of all the SST products used may smooth signals that are very transient in nature and 4/the model is initialized with horizontally homogeneous conditions which are unlikely to exist in reality, particularly at the surface.

Overall, although the flat bottom models are prone to downwelling overshooting, they perform well at reproducing the main events observed. The extended model tends to out-perform the local model during large events occurring in Fortune Bay notably during 14–16 July and 20–23 September; suggesting a possible remote effect captured by the former. In the latter cases, strong wind shifted swiftly from negative to positive along-shore forcing (NE to SW). The absence of the downwelling event of July 9th from the local model also suggests possible remote effect.

Linear correlations between observed and modeled 4°C isotherm's depth as well as along-shore currents were computed to quantify the agreement. The analysis used unfiltered, raw signals; therefore making it a direct comparison between observations (which include the full variability of the ocean) and model (which is idealized). In July, correlation coefficient squared *r*² values of 0.1 (F3B01-05) to 0.6 (F3B08-06) are found with the isotherms using the local domain; increasing to 0.6–0.7 using the extended domain (*p*-values <0.01). Adjusting for small phase lags (2 and 4 hr; local and extended model, respectively) *r*² values increases to 0.2–0.7 (local) and to 0.6–0.8 (extended). Correlations are lower with the currents, but still significant (*p*-values <0.01) and equal to 0.5 for both the local and extended model results (F3B08-06). No improvement were found using lagged correlations on along-shore currents from either the local or extended models. In September, correlations were performed on day 9–29 window, as for the zero-crossing analysis performed earlier; taking into account the probable influence of past events on the first few days of the simulation and of complex signal interactions or internal mixing toward the end of the series. Overall, *r*² values are lower for the September events, however, only reaching about 0.3 (local) to 0.4 (extended) for the 4°C isotherm depth and 0.2 (extended) to 0.3 (local) for the along-shore currents across all sites (*p*-values <0.01). Lagged correlations slightly improved the isotherm depth correlations of the extended model to 0.4 (with a lag of about 10 hr) and improved the currents from 0.2 to 0.4 (extended; 9 hr lag) and from 0.3 to 0.4 (local; 5 hr lag). Thus, for this period, the extended model did not improve the results. RMSE values on the order of 6–7 m for the isotherms and 0.1 m/s for the currents are found for both July and September
events (and for both local and extended model results). In all cases but for the first event of July with the local model and with the extended model of July at F3B08-06 (both events), the observations were found to be leading the model; by a few hours, generally. Observation gaps affected the results; particularly at F3B08 where the 4°C isotherm outcropped the observations for a large part of the series in July (8–16), that is times when the isotherm was located above the shallowest observation point (located around 20 m at F3B08). The lack of along-shore current data at F3B01, 05 and 07 was also a limiting factor.

### 3.3. Idealized Model Cases

To investigate the effect of wind forcing direction on the response observed in Fortune Bay and untangle local versus remote effects, idealized wind conditions were applied using summer hydrographic conditions. Only results from the extended mesh are considered; local versus remote effects were investigated by applying wind forcing on a specific area of the mesh (Fortune Bay vs. Placentia Bay, respectively; see Figure 2).

Four main directions were chosen, representative of the main along and across-shore directions of Fortune Bay: northeast (NE), northwest (NW), southwest (SW) and southeast (SE). Note that while NW and SE are across-shore directions for Fortune Bay's main basin they are also along-shore directions for Belle Bay. For each direction, a 10 m/s wind speed (0.14 N/m² stress) was applied for 2 days with a linear ramp-up and ramp-down period of 6 hr to each end (i.e., 6 hr ramp-up, 36 hr full speed and 6 hr ramp-down). This can be considered as a strong, yet comparable, forcing scenario to the observations (Figure 4) and consistent with the findings of previous studies on typical cyclone activity in the region (Donnet et al., 2022; Plante et al., 2015).

Sensitivity tests were performed using a wind speed of 5 m/s (0.04 N/m²) and using wind of same intensity (10 m/s) but lesser duration (1 day; same ramps than with the 2 days scenario) and resulted in much weaker responses for both scenarios and in both isotherms displacement and along-shore currents, as one would expect (see Figure S13 in Supporting Information S1 for illustrations). The propagation speed is comparable for all scenarios but the pulse generated (either upwelling under NE wind or downwelling under SW wind) is of smaller duration for both weaker and shorter wind forcing scenarios (by about a day at F3B08). These results indicate the need for relatively strong winds (≥10 m/s) and of sufficient duration (>1 day) to generate the type of response most visible in Figure 4 and presented herein.

#### 3.3.1. Homogeneous Wind

Figure 7 (top panels) illustrates the water column responses to SW and NE along-shore winds applied homogeneously on the whole extended domain. Wind was applied from run time $t = 0$ up until run time $t = 2$ days.

A SW wind forcing (left panel) initially generates a downwelling at F3B01&05 and upwelling at FB03&06 (first two days), consistent with expected Ekman transport. The amplitude of the response is about 5 m (F3B01) to 10 m (F3B05). This forced downwelling pulse, that is generated during the wind forcing, rapidly propagate cyclonically, reaching F3B08&04 during day 2, and F3B03&06 during day 3; therefore taking about 2 days to travel from F3B01 to F3B06. The downwelling pulse, which is about 2 days long, is followed by a much broader and somewhat weaker upwelling one which last about 5 days and which is followed by another downwelling pulse (from $t = 7$ days at F3B01), noticeably weaker also and more diffuse than the first downwelling one.

Under a NE wind forcing (right panel) an opposite response is initially felt: upwelling at F3B01&05 and downwelling at F3B03&06 ($t = 1$ day), while isotherms stay about flat at both F3B08&04. The amplitude of this initial response is about 15 m at F3B01 to 20 m at F3B05. About ½ day before the wind cease ($t = 1.5$ days), the upwelling signal arrives at F3B08 and then F3B04 and steadily develops for about 2–3 days. Shortly before the wind ceases a sharp downwelling is being generated at F3B01 (first) and F3B05 (about ½ day later). This downwelling pulse propagates cyclonically, clearly losing strength while doing so; the temperature front broadens (in time) and associated surface currents occupy less vertical space (from more than 50 m at F3B05 to 20 m at F3B06). In contrast, the upwelling pulse preceding the downwelling pulse seems to retain its strength, in both isotherm displacement and currents, from F3B08 to F3B06 (F3B04 currents being weaker is all simulations due to its position with respect to the jet; an effect of the coastline complexity of Belle Bay). The event, from its upwelling to downwelling phase (outgoing and ingoing flow) last about 5–6 days at all sites and it takes about 3 days for the downwelling pulse to travel around the bay from F3B01 to 06. Following the passage of this downwelling pulse, the isotherms gradually rise to return at the initial state.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Fortune Bay idealized along-shore wind model forcing results (Southwest, left panels, and Northeast, right panels, wind forcing). Isotherms 2, 4 and 12°C are represented (black lines) over along-shore currents (blue to red colors, positive into the bay) at mooring locations F3B01, 05, 08, 04, 03, 06, and 02 (cyclonic distribution around the bay). X-axis represent run time elapsed, in days.</figcaption></figure>

Two main and distinct downwelling dynamics can thus be seen: a “forced” pulse, generated during a SW wind event and a “relaxation” pulse, generated right after a NE wind event ceased. In both cases, the upwelling phase occurring before (under NE) or after (under SW) the downwelling is associated with broader (time-wise) and
<table><caption>**Table 2**
Lagged Cross-Correlation Model Results (Extended Mesh; Idealized Wind)</caption><thead><tr><th>Mooring pair (km)</th><th>Wind forcing</th><th>r (δt = 0)</th><th>r<sub>max</sub> (%var)</th><th>δt (r<sub>max</sub>) (d)</th><th>c (m/s)</th><th>DWdiff (m) (% change)</th></tr></thead><tbody><tr><td>F3B01-06 (180)</td><td rowspan="3">SW Homogeneous</td><td>-0.35 (12%)</td><td>0.60 (36%)</td><td>-1.8</td><td>1.2</td><td>+14 (+280%)</td></tr><tr><td>F3B01-08 (120)</td><td>0.45 (20%)</td><td>0.74 (55%)</td><td>-0.7</td><td>2.0</td><td>+15 (+300%)</td></tr><tr><td>F3B08-06 (60)</td><td>0.45 (20%)</td><td>0.96 (93%)</td><td>-1.2</td><td>0.6</td><td>-1 (-5%)</td></tr><tr><td>F3B01-06 (180)</td><td rowspan="3">NE Homogeneous</td><td>-0.64 (41%)</td><td>0.81 (65%)</td><td>-3.2</td><td>0.7</td><td>-7 (-47%)</td></tr><tr><td>F3B01-08 (120)</td><td>-0.23 (5%)</td><td>0.76 (58%)</td><td>-2.1</td><td>0.7</td><td>-1 (-7%)</td></tr><tr><td>F3B08-06 (60)</td><td>0.57 (31%)</td><td>0.95 (91%)</td><td>-1.1</td><td>0.6</td><td>-6 (-43%)</td></tr><tr><td>F3B01-06 (180)</td><td rowspan="3">SW FB only (local DW)</td><td>-0.50 (25%)</td><td>0.63 (40%)</td><td>-2.1</td><td>1.0</td><td>+15 (300%)</td></tr><tr><td>F3B01-08 (120)</td><td>0.57 (33%)</td><td>0.89 (80%)</td><td>-0.9</td><td>1.5</td><td>+15 (300%)</td></tr><tr><td>F3B08-06 (60)</td><td>0.25 (6%)</td><td>0.91 (83%)</td><td>-1.3</td><td>0.5</td><td>0 (0%)</td></tr><tr><td>F3B01-06 (180)</td><td rowspan="3">NE FB only (local UW)</td><td>-0.40 (15%)</td><td>0.74 (55%)</td><td>-3.2</td><td>0.7</td><td>+2 (+11%)</td></tr><tr><td>F3B01-08 (120)</td><td>0.32 (10%)</td><td>0.84 (70%)</td><td>-1.6</td><td>0.9</td><td>+2 (+11%)</td></tr><tr><td>F3B08-06 (60)</td><td>0.55 (31%)</td><td>0.96 (92%)</td><td>-1.6</td><td>0.4</td><td>0 (0%)</td></tr><tr><td>F3B01-06 (180)</td><td rowspan="3">SW PB only (remote UW)</td><td>0.16 (3%)</td><td>0.99 (97%)</td><td>-3.0</td><td>0.7</td><td>-2 (-15%)</td></tr><tr><td>F3B01-08 (120)</td><td>0.67 (44%)</td><td>0.96 (93%)</td><td>-1.6</td><td>0.9</td><td>-2 (-15%)</td></tr><tr><td>F3B08-06 (60)</td><td>0.67 (45%)</td><td>0.99 (98%)</td><td>-1.4</td><td>0.5</td><td>0 (0%)</td></tr><tr><td>F3B01-06 (180)</td><td rowspan="3">NE PB only (remote DW)</td><td>0.31 (10%)</td><td>0.95 (90%)</td><td>-2.5</td><td>0.8</td><td>+1 (+5%)</td></tr><tr><td>F3B01-08 (120)</td><td>0.62 (39%)</td><td>0.95 (91%)</td><td>-1.6</td><td>0.9</td><td>+4 (+31%)</td></tr><tr><td>F3B08-06 (60)</td><td>0.86 (74%)</td><td>0.99 (97%)</td><td>-0.8</td><td>0.9</td><td>-3 (-18%)</td></tr></tbody></table>

Note. *r* is the Pearson correlation coefficient. Lag (δt) is negative when first mooring of the pair is leading the second (e.g., F3B01 leading F3B06). *c* = phase speed calculated as a distance between mooring pair (indicated in bracket) divided by δt. DWdiff = Downwelling amplitude difference between the mooring pair; a positive sign indicate second mooring observed a larger downwelling than the first (e.g. F3B06 downwelling resulting from SW homogeneous forcing is larger than F3B01 one by 14 m).

weaker currents (and/or more constraint vertically). The relaxation pulse is characterized by a rather sharp front at its genesis (F3B01 & 05) which appears to flatten fairly quickly as it propagates around the bay. In contrast, the forced pulse appears to increase in strength (isotherms vertical displacement) during its propagation. The forced pulse is also appreciably quicker, taking about 2 days to propagate from F3B01 to F3B06 (180 km) versus 3 days for the relaxation pulse to travel the same distance; thus a factor 1.5 in phase speed (0.7 m/s vs. 1 m/s).

Responses from across-shore winds (NW and SE) are presented in the Figure S14 in Supporting Information S1 and are much weaker. Results from SE stress resemble that of SW (with about 1–2 days delay at all sites) but is much less dynamic (factor 2 or more) and results from NW show small and short downwelling occurring during the wind event at F3B01&05 (while F3B08&04 are upwelling) followed by the formation of a broad (2–4 days) and weak upwelling pulse at F3B01&05 and of a downwelling pulse from F3B08 to F3B06 (traveling cyclonically). As expected, however, Fortune Bay's main basin along-shore stress response is much larger.

Similar cross-correlations than for the validation exercise were performed on the SW and NE forcing scenarios and are summarized in Table 2 (see also Figure S15 in Supporting Information S1 for illustrations). The results of those cross-correlations show that while the propagation of the signal has a constant phase speed under a NE wind forcing event (0.6–0.7 m/s) it varies significantly within the bay under a SW wind forcing event (from 2 to 0.6 m/s or more than a factor 3 from F3B01-08 to F3B08-06). The amplitude of the response also differs between the two scenarios: while it increases significantly from F3B01 to F3B06 under a SW forcing (+280%) it decreases under a NE forcing (–47%). These results from idealized scenarios compare well with those of the real wind from July 2016 which indicated the same order in phase speed and its variability between the two main events identified and an enhancement of the signal during the first event versus an attenuation during the second event (Table 1). This suggests that the propagation of the first event of July would be dominated by the initial SW wind forcing response (downwelling favorable, locally) while the propagation of the second event of July would be dominated by the initial NE wind forcing response (upwelling favorable). It also indicates that while the propagation speed of
an upwelling response (both forcing and relaxation phase) are about the same than the free, mode 1, long internal wave, the propagation speed of a downwelling response is much faster (by a factor 2).

### 3.3.2. Local Versus Remote Wind

To isolate the possible remote effects of Placentia Bay, located upstream from Fortune Bay in a cyclonic sense of propagation, same along-shore wind stress scenarios were run using the extended mesh but applying the stress on Fortune Bay area only ("FB only") and on Placentia Bay only ("PB only").

The results of a SW wind stress applied locally (FB only, Figure 7 left middle panel) are very similar to the results of the homogeneous wind. The first, and strongest, downwelling generated is essentially of the same strength (isotherms amplitude and associated currents) and appears to travel at the same speed than under a SW wind stress applied regionally (upper panel). The following broad upwelling is, however, slightly weaker (both in terms of isotherms migration and currents) than the one that occurs under homogeneous wind and no second downwelling appears either (after $t = 7$ days at F3B01). In contrast, the results of a local NE wind stress (right middle panel) are quite different. While the first upwelling is similar (in both strength and duration) the downwelling pulse that follows is markedly less strong and visibly broader than under the homogeneous wind scenario. This pulse also occurs later than during the homogeneous scenario, reaching F3B01 (and all the other sites) about 0.5–1 day later.

With a wind stress applied on PB only, the bottom panels of Figure 7 essentially show pictures of what a sub-traction of local wind results from the homogeneous wind results would provide. Under a SW wind stress, a broad and weak upwelling event occurs from $t = 2$ days at F3B01 and ends by a downwelling pulse which occurs after $t = 7$ days. Under NE wind, a strong and fairly broad downwelling event (about 20 m range, 4 days long) appears near the end of the wind event at F3B01 ($t = 1.5$ days) and propagates around the bay as under an homogenous forcing although a little quicker (about 1 day less for the pulse to reach F3B06 from F3B01).

Cross-correlation analyses results (Table 2 and Figures S16 and S17 in Supporting Information S1) show that a locally generated downwelling event (FB only, SW wind scenario) is the signal that propagates the most rapidly (2 days to reach F3B06 from F3B01) and is also the signal changing the most during its propagation with a phase speed propagation decreasing by a factor of 3 from F3B01-08 to F3B08-06 (1.5 to 0.5 m/s) and a downwelling amplitude increasing by 300%; similarly to the homogeneous wind scenario and the first event observed in July 2016. In contrast, a downwelling event generated remotely (PB only, NE wind scenario) propagates at a near constant speed (~0.8 m/s), and undergoes little amplitude change (8% between F3B01&06). Upwelling scenarios, whether locally or remotely generated (NE, FB only and SW, PB only, respectively) do not show much changes in amplitude (11%–15%) but do show a change in propagation speed, decreasing by a factor of 2 from F3B01-08 to F3B08-06 (from 0.9 to 0.5 m/s, respectively).

These scenarios confirm that additional downwelling and upwelling events generated in Placentia Bay likely propagate into Fortune Bay and interact with existing local conditions; thereby either enhancing existing conditions (e.g., upwelling phase following the first downwelling pulse under SW forcing) or adding a separate event a few days later (e.g., second downwelling pulse under SW forcing). The largest difference in response is seen under the NE wind forcing scenario which results in a strong enhancement of the downwelling pulse, propagating around the bay. The difference between local and homogeneous scenarios is on the order of a factor 2 with this forcing, in both vertical migration of the thermocline and associated current pulse (20 vs. 40 m and 0.25 vs. 0.5 m/s at F3B01&05, respectively). The timing of the main downwelling pulse is also affected (occurring earlier under homogeneous wind), suggesting interactions between the two responses (i.e., local and remote). The results of cross-correlation analyses further points toward likely interactions between the local and remote response during a NE wind event. Hence, during such forcing, the local upwelling event slows down within the head of the bay (from 0.9 m/s between F3B01&08 to 0.4 m/s between F3B08&06) while the remote, downwelling, event travels at a constant speed all along (0.8–0.9 m/s); indicating a likely interaction (i.e., a downwelling pulse "catching-up" on an upwelling pulse). Given that the time for the downwelling pulse generated in Placentia Bay to reach Fortune Bay also roughly correspond to the time by which the wind stress applied decreases to zero (1.5 days), downwelling enhancement can also be expected.
### 3.4. Horizontal Patterns Under Idealized Wind Forcing

To determine the origin and scale (along and across-shore) of the downwelling and upwelling events, and better understand their propagation, surface maps illustrating the thermocline depth and currents of the surface layer were made (Figures 8 and 9). Thermocline depth variation is represented using the depth anomaly of a selected isotherm. Same isotherm and depth-average procedure as for the validation exercise were used, that is 4°C isotherm depth. Depth anomaly was calculated using a value of 35 m at rest (i.e., 4°C depth value from the climatology profile used to initialize the model) and is positive downwards (i.e., downwelling are red and upwelling are blue).

Figure 8 shows the response under the idealized SW wind forcing scenario. Six days are represented from when wind stress was fully applied (i.e., model run elapsed time = 1 day = 18 hr after ramp-up). Clear downwelling and upwelling areas, due to Ekman transport, are visible along the Burin peninsula shores (Fortune Bay side and Placentia Bay side, respectively). The onset of a downwelling is nearly immediate along the Fortune Bay side of the Burin peninsula (as seen at F3B01 and F3B05 in Figure 7) and is already propagating northward after 1 day. Behind this downwelling, the upwelling area occurring on the southern shore of the Burin Peninsula and along the Placentia Bay side increases in strength by day 2. After 2 days, the downwelling is concentrated in the north-eastern end of Fortune Bay and in Belle Bay and is exiting the latter at $t = 3$ days. Meanwhile, the following upwelling propagates into Fortune Bay and is, itself, followed by another downwelling coming from the northern part of Placentia Bay. Strong currents are clearly associated with the downwelling and upwelling areas, and enhancement of both thermocline migration and upper-layer current appear to occur in Belle Bay. The cross-shore length scale of the features is about 5 km; consistent with the estimate of internal Rossby radius presented earlier. The long-shore scale of the wave (i.e., downwelling + upwelling length) is on the order of twice the length of the Burin Peninsula, that is about 300 km; also consistent with previous estimates based on observations.

Under a NE wind forcing scenario (Figure 9), clear upwelling and downwelling areas are also visible along the Burin peninsula shores at $t = 1$ day; the situation being reversed from that of the SW scenario, that is upwelling on Fortune Bay side and downwelling on Placentia Bay side. As under the SW scenario, the downwelling and upwelling areas are clearly associated with the strongest currents. At $t = 1$ day, the downwelling has, in fact, already started to propagate and its “head” is located at the southern tip of Fortune Bay. A day later ($t = 2$ days) the upwelling area moved up into BB while the downwelling is moving around the tip of the peninsula and is starting its propagation into Fortune Bay; F3B01 site being located close to the node between the upwelling and the downwelling. At $t = 3$ days, the downwelling has established itself along half the Fortune shore of the Burin peninsula. The northward progression of this downwelling continues at $t = 4$ days and it reaches Belle Bay (F3B08 & 04) at $t = 5$ days; turning cyclonically around its shores until exiting at run $t = 6$ days. The propagation of the upwelling illustrated here (Figure 9) and thus of the downwelling following it, is clearly slower than the downwelling locally generated under SW wind (Figure 8). Cross-shore and along-shore scales are however comparable with that of the SW scenario (about 5 km cross-shore and 300 km along-shore).

## 4. Discussion

The objectives of this paper are to: 1/determine the nature of the dominant process acting in Fortune Bay during the stratified seasons and expressed as sub-inertial, baroclinic signals (Donnet et al., 2022); 2/determine the origin of this process (forcing and geographic) and 3/describe its propagation within the fjord. We will now discuss the main results considering these objectives and what is known from the literature (theoretical or experimental studies).

### 4.1. Nature of the Process

Fortune Bay's stratification and topographic characteristics, as embedded in the Stratification parameter $S$ (i.e., ratio of internal Rossby radius to shelf-slope width) indicate that sub-inertial, coastally trapped motions, would take the form of baroclinic Kelvin waves in most of the fjord ($S \gg 1$). This hypothesis was tested using a fully non-linear, 3-dimensional, flat bottom numerical model initialized by climatological stratification and forced by wind only (both horizontally homogenous fields). This setup should only allow the CTWs generation of Kelvin nature in the sub-inertial band. Our model results show a rapidly responding system to wind forcing; generating Ekman transport and associated, geostrophically balanced, coastal jet near the surface (Charney, 1955) and propagating signals around the bay (Figures 7–9). These signals take the form of downwelling and upwelling
SW wind forcing

<figure><img src="image_10.png" /></figure>

**Figure 8.** Isotherm 4°C depth anomaly and upper layer current response under SW idealized along-shore wind forcing (2 days forcing). Positive anomaly (red) represents downwelling while negative anomaly (blue) corresponds to upwelling conditions. Upper layer current is depth-averaged from the surface down to the 4°C isotherm depth. For clarity, the resolution was reduced by a factor of 5 to draw the arrows (currents). Black boxes represent the mooring sites listed in Figure 1. X and Y axis are Eastern and Northern UTM coordinates (x10⁵ and x10⁶ m, respectively).
NE wind forcing

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Isotherm 4°C depth anomaly and upper layer current response under NE idealized along-shore wind forcing (2 days forcing). Positive anomaly (red) represents downwelling while negative anomaly (blue) corresponds to upwelling conditions. Upper layer current is depth-averaged from the surface down to the 4°C isotherm depth. For clarity, the resolution was reduced by a factor of 5 to draw the arrows (currents). Black boxes represent the mooring sites listed in Figure 1. X and Y axis are Eastern and Northern UTM coordinates (x10⁵ and x10⁶ m, respectively).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Isotherm 4°C depth anomaly (iso4°C) at F3B01 (top) and F3B06 (bottom) and under various idealized model scenarios. SW FB only = southwest wind forcing applied on Fortune Bay area only, SW PB only = southwest wind forcing applied on Placentia Bay only, FB + PB = sum of FB only and PB only scenarios, SW whole = southwest wind forcing applied over the whole model domain (i.e., over FB and PB areas); NE = northeast wind forcing. Note: series were low-pass filtered using a 24 hr window running-average.</figcaption></figure>

events associated with strong baroclinic currents which clearly dominate the response and have the characteristics of iKWs (e.g., unidirectional propagation and across-shore scale on the order of a Rossby radius). Owing to the shape of the bay, which is semi-opened on its western side, most of the energy exit before reaching its mouth, that is before reaching F3B02 (Figures 8 and 9); thereby precluding excitation of potential natural oscillations (seiche) within the surface layers. Higher frequency signals (near-inertial) are produced and attributed to Poincare-type waves. While visible from the model results but not observed by in situ measurements (most likely due to their proximity to the coast), those latter signals do not dominate the response (Figure 6). The model was shown to be capable of reproducing up to 80% of isotherms oscillations (i.e., downwelling and upwelling signals) and up to 50% of the upper layer along-shore current variability (Figures S8–S11 in Supporting Information S1); strongly suggesting that iKWs dominate the response to wind forcing in Fortune Bay during summer.

Our results are generally consistent with those of Yao (1986), de Young et al. (1993) and Davidson et al. (2001) in the Trinity Bay—Conception Bay system which has similar geographic and stratification characteristics (seasonally stratified wide and deep bays, mainly oriented SW-NE on two opposite coasts; Figure 1).

The existence of CTWs dynamics, which have recently been observed around the nearby archipelago of SPM (Lazure et al., 2018) should not be excluded, however, particularly in the outer part of Fortune Bay where the shelf-slope widen. At F3B01 and 05 locations, for instance, the shelf-slope width is on the order of 10–15 km, leading a stratification parameter of 0.4–0.6 (thus, <1). The shelf is also noticeably larger and more complex (with the presence of islands) on the Placentia Bay side (Figure 1). The presence of a non-negligible shelf-slope region would have 3 main consequences (see Brink, 1991 for a review of CTW characteristics):
* the modal structure of the signals would be more complex (on the vertical) with the nodes extending offshore (see Figure 6 of Masoud et al., 2019 for a recent and illustrative investigation of this in the Caspian Sea),

* the phase speed would decrease (for the baroclinic signals),

* and a larger barotropic signal would be observed (e.g., on sea level).

The presence of CTW-like dynamics may, at least partially, explain the larger differences found between the observations and our model results at F3B01 and F3B05 (Figure 6 and Figures S8–S11 in Supporting Information S1). A number of model runs were attempted using a realistic bathymetry but proved to be unsuccessful due to over-mixing issues. Keeping stratification over steep slopes and in the presence of large vertical isopycnal variations such as presented here is a well known challenge for terrain-following coordinates models such as FVCOM (see Haney, 1991; Mellor et al., 1994 for a discussion on this). Despite increasing the horizontal resolution down to 100 m and smoothing the bathymetry to reduce the gradients, experimenting with a range of *dH/H* of 0.3–0.5 (where *dH* is the maximum depth change and *H* is the mean depth of any given mesh cell; see Foreman et al., 2009) we were not able to resolve this issue satisfactorily.

## 4.2. Origin of the Process

Given the close representation of the (raw) observations by the model, which is solely forced by wind, we can deduce that the latter is the main forcing mechanism responsible for the dominant sub-inertial and baroclinic dynamics observed in Fortune Bay in summer (with periods of the order of a few days). This is consistent with and complement previous observations-based findings which showed a modest contribution of the tides (9%–34%; weakest at the head, in Belle Bay, and strongest at F3B02) and a weak mean seasonal circulation (order of 1–5 cm/s; Donnet et al., 2022).

By implementing the model and forcing on two geographical areas, one centered on the fjord (local area) and one including the neighboring bay to the east (extended or remote area), we show that the response observed is both from local and remote, that is neighboring bay, origin. Most of the variability appears to be locally generated from southwesterly winds which result in rapidly propagating downwelling pulses around the fjord (about 2 days propagation time) as observed in early July 2016 and in September 2016 (Figure 5). The largest events observed such as the one of 13–20 July 2016, however, are generated by winds shifting from the northeast to the southwest which result in an upwelling event generated in the fjord and a downwelling event generated in the neighboring bay. If timing is right and that the remotely generated downwelling event arrives in the fjord at the same time that the locally generated upwelling is relaxing, for example due to wind dropping or changing direction, both signals seem to add-up and a larger downwelling occurs (Figure 6a). Results from idealized scenarios, used to better understand the process, show that it takes about 1.5 days for a remotely generated downwelling event to arrive in Fortune Bay at our sampling site F3B01 (Figure 7). Considering a typical cyclone duration of about 4 days in the region (Plante et al., 2015), a 2 days duration for a 180° shift in wind direction, and associated downwelling enhancement during NE-SW wind events, could be quite common; as seen during the periods selected for our study (July and September 2016; Figure 5).

Although much weaker, remote effects from SW winds also occur and are mainly expressed as a broad upwelling event, about 6 days in duration, followed by a downwelling pulse propagating in the fjord about 5 days after a wind event (i.e., from *t* = 7 days at F3B01, Figure 7). While the upwelling phase comes from the western side of Placentia Bay, along the Burin peninsula, the downwelling pulse comes from the eastern side of the bay (Figure 8 and Figure S18 in Supporting Information S1 for a broader view). Similarly, a weak upwelling signature, propagating from that shore is also apparent after a NE wind event (seen in Figure 9, *t* = 3–6 days snapshots, in particular) and would, should no counter-forcing mechanism or complete dissipation to occur, make its way into the fjord. Our model uses a much simplified northern and eastern coastline of Placentia Bay, however, and it is probable that these signals from the eastern part of the domain are attenuated with the complexity of the real coastline.

Yet, given the complexity of the coastline, wind from any direction can generate a response in Fortune Bay. The scale of the response is determined by the length of the coast that is oriented along the wind and where the offshore scale allows Ekman transport to take place, that is where it is not small relative to the internal Rossby radius (e.g., Crépon & Richez, 1982). Hence, additional model runs show how winds from the NW and SE can induce upwelling and downwelling, respectively, around the southern end of the Burin Peninsula which are about half the length of those induced by NE and SW winds (Figure S18 in Supporting Information S1). The wavelength of the
response is directly determined by the length of the coast oriented with the wind but those simulations also showed a factor 2 less in strength of those cross-shore wind responses from that of the along-shore winds (being isopycnal vertical variation or baroclinic, along-shore, currents; Figure S14 in Supporting Information S1).

Therefore, the dynamic of Fortune Bay is likely to be the result of a combination of responses occurring at different places and time in both Fortune Bay and Placentia Bay under a continuously variable wind field. The strength and duration of the response being a function of forcing strength, duration and direction (Figures S13 and S14 in Supporting Information S1).

### 4.3. Signal Propagation

Having determined the nature of the process as well as its forcing and geographic origin, a last important piece of the puzzle is to understand its propagation. We will attempt to do so by further describing the observations and combining the model results.

The most striking propagation characteristic found from both observations and model simulations is the coherence of the signal, propagating cyclonically around the bay (Figures 5 and 7) and supporting the hypothesis of a coastally trapped wave of Kelvin properties. The second most striking aspect concerns the variation in phase speed and amplitude of the signal (summarized in Tables 1 and 2). The last notable observation was the apparent change of signal frequency from the outer to the inner part of the bay during the more frequent event of September (factor of 2 change).

Results from the model using idealized wind forcing suggest two main things: that the first downwelling event observed in July was dominated by the propagation of a locally forced and rapidly propagating wave while the second downwelling event observed that same month was dominated by a wave propagating more slowly (about half the speed of the former event) and that was likely the result of an interaction between a locally generated response (upwelling) with a remotely generated one (downwelling). These results also suggest that there must exist factor(s) influencing the amplitude of the response during its propagation which do not act similarly during a locally forced downwelling (large increase) versus a remote downwelling response following a locally forced upwelling (sizable decrease). The results of these modeling scenarios are summarized and compared in Figure 10 (see also Figures S16 and S17 in Supporting Information S1 for more details).

Figure 10 shows that a SW wind, solely applied on Fortune Bay (FBonly line) generates a rather short downwelling, about 2 days duration, at F3B01 (panel A) followed by a long plateau of slightly upwelled waters (–5 m isotherm depth anomaly). The shape of this wave is “solitary-like,” that is trough only with no crest, and is 5 m in amplitude. This downwelling peak then increases drastically to attain a maximum of 20 m amplitude at F3B06 before rebounding somewhat less vigorously toward a neutral position and then rising slowly after $t = 6$ days (panel B). Overall, the downwelling duration increases from 2 days at F3B01 to about 4 days at F3B06. The phase speed of this event changes drastically, from 1.5 m/s between F3B01 and 08 to 0.5 m/s between F3B08 to 06 (Table 2); similarly to the SW homogeneous wind scenario and comparable with the observations of the first event of July 2016 (Table 1). Thus, with a phase speed decreasing by a factor 3 between F3B08 and F3B06 but a period (duration) only doubling, the wavelength of this event must have reduced to about 2/3 from its original size. Simultaneously, a SW wind applied on Placentia Bay only (PBonly line) generates a much broader upwelling event at F3B01, of about 6 days in duration, followed by a slow downwelling phase. Arrived at F3B06, this upwelling event lost a little of its strength, decreasing in amplitude by about 15% from F3B01 (from about 13 to 11 m) but stays about the same in duration; thus retaining much of its shape (and wavelength). This upwelling event also slowed down along the way, by a factor 2 from F3B01-08 to F3B08-06 (0.9 to 0.5 m/s; Table 2). Linearly adding those two signals together (FB + PB dash lines) results in a pattern similar to that of the homogeneous SW wind forcing scenario applied to the whole model domain (SW whole) at both sites, indicating a near-linear interaction between the two events.

A local NE forcing (FBonly line; Figures 10c and 10d) also generates a short but large upwelling (in amplitude and in comparison to the corresponding SW result; 18–20 m rise vs. 5 m down, respectively). This event broadens dramatically from a duration of about 3 days at F3B01 to more than 8 days once arrived at F3B06 all the while retaining its large amplitude. Given that its phase speed decreased by a factor 2 between F3B08 and 06 (from 0.9 m/s between F3B01&08 to 0.4 m/s from F3B08&06; Table 2) the wavelength of this event thus increased to about 3/2 its original size (using an event duration of 9 days at F3B06). On the other hand, the downwelling event
generated remotely (POnly lines) keeps its shape all along from F3B01 to F3B06 (about 12.5 m amplitude and 6 days duration) and propagates at a constant speed (about 0.8 m/s; Table 2). This propagation speed is, however, slightly higher than the locally generated upwelling one (2.5 days to propagate from F3B01 to 06 vs. 3.2 days for the upwelling). The main difference in speed occurs between F3B08&06 (0.4 m/s for an FB event vs. 0.9 m/s for a PB event; Table 2) and indicates that interaction between those two events may occur. Adding the signals together (dashed line) leads to a result markedly different from the whole domain forcing scenario (NE whole) this time, particularly at F3B06; indicating that non-linear effects are important in the interaction of the responses from a NE forcing (local with remote).

While the observed and modeled propagation patterns are complex, the overall propagation speed during the event periods considered depend on whether downwelling or upwelling dominates, the former propagating faster than the latter. Both our observations and model results show steeper downwelling fronts than upwelling ones (Figures 5–7 and 10), the steepest front we observed and modeled occur when a remote downwelling follows a locally generated upwelling (12–20 July event and “NE whole” scenario); suggesting important non-linear interactions between independent signals.

The linear and inviscid equations of the iKWs fail to explain these differences in phase velocity, since iKWs are non-dispersive and the propagation speed is independent of the wave amplitude (which is assumed to be very small in relation to the depth). Its expression is $c_0 = \sqrt{g'h^*}$ with the equivalent depth $h^* = (h_1 * h_2)/((h_1 + h_2))$. In our case, the thermocline depth at rest is $h_1 = 35$ m, $h_2 = 300–35$ m and the averaged value of $g' = 0.02 \text{ m}^2/\text{s}$ give linear phase velocity of $c_0 = 0.77 \text{ m/s}$. This value is the order of magnitude of the observed phase velocity but does not differentiate upwelling from downwelling.

It is therefore necessary to consider the role of the nonlinear terms. Bennett (1973) shows that non-linear effects steepen freely propagating iKWs. Clarke (1976) further argues that their phase speed increases (decreases) when the pycnocline is displaced upward (downward). Latter, Yamagata (1980) provides a solution based on mass and potential vorticity conservation for the propagation of sharp downwelling fronts (his Equation 3.10) which leads to a shock wave equation and gives for an average thermocline depths in downwelling conditions $c = c_0 * [(h_d)/2h_1]$. This formulation makes a positive dependency of the phase speed to the downwelling amplitude on $h_d$ and values of 10–20 m would lead to a phase speed increase of 15%–33%; broadly consistent with our results and support the idea of an interaction between local and remote signal in Fortune Bay.

In September, good performance of the local model indicates the dominance of local responses to forcing (Figure 6). The situation is rather complex, however, since that while the 3 main downwelling events propagating from F3B08 to F3B06 can be understood as (mainly) local responses resulting from the 3 main SW wind events, it is unclear why higher frequency signals would occur downstream at F3B01&05 (Figure 5). Remote effects, as described above, should somewhat temper locally generated downwelling by bringing upwelling pulses about 2 days after each wind event and last for about 5 days after (Figures 7 and 8). These upwelling are indicated by the rising of the 2°C in (e.g., from 13, 18, and 22 September) but the first two are rather quickly followed (~1–2 days) by another downwelling pulse from unknown origin (14–15, 19 September). Remote effect from the east side of Placentia Bay, expressed as a downwelling arriving 5 days after the end of a wind event (Figure 7) is therefore unlikely given these short intervals. Possibly, and given the frequency of wind events during this period of the year (Figure 4), the system was far from being at rest at the beginning of the series studied and those pulses may be the remnants of previous wind events. As such the system has an “effective memory” from previous forcing (see Beletsky et al., 1997 for a use of this terminology). Under SW wind, for instance, the effects of 1 event of 2 days duration could last for more than 2 weeks according to the results presented herein (2 days forcing +2 days propagation +5–6 days first remote response +5–6 days for the second remote response). Yet, the “low-pass” filtering of those frequent events occurring in the outer part of the bay (F3B01&05) by the inner part of the bay (F3B08-06) is also unclear. Since the length of Belle Bay is about a quarter of that of Fortune Bay (30 vs. 120 km, respectively), resonance effects could be suspected. However, this would translate into an amplification of the signal and a periodicity of about 2.5 days (with a natural mode phase speed of 0.6 m/s). Neither effects are seen in the observations: the amplitude of the events are comparable across sites and the periodicity is of 6 days (3 events in 20 days). Possibly, the large slow-down of locally generated downwelling event in the inner part of the bay described above (factor 3) could have an influence and effectively “merge” several fast traveling pulses arriving from the outer bay. A more throughout analysis of this latter possible interaction would be, however, necessary to better elucidate these observations.
One can note that in many of our estimates of phase velocities, both forced and free waves are present. While estimating phase speeds from a forced field is complex, we believe our approach remains robust. Our idealized scenarios, which involve a fixed 2-day forcing period, leave the waves propagating freely afterward, allowing us to isolate wave behavior once the forcing ceases. Additionally, the comparison between locally forced upwelling and downwelling (with the latter propagating faster) helps to highlight the distinct dynamics of the forced field. Despite the time-varying nature of the real-world forcing, the close match between observed and modeled phase speeds, particularly the faster propagation of downwelling, suggests that our wave speed estimates are still valid to a first order.

## 5. Conclusion

In this paper we have investigated oceanic responses to variable wind forcing in Fortune Bay, a broad mid-latitude fjord in Newfoundland, using in situ observations and numerical modeling. Both observed data and model simulations show large sub-inertial baroclinic motions. They are dominated by coastal-trapped waves of baroclinic Kelvin nature, propagating with the coast on the right. They are generated locally in Fortune Bay and remotely in neighboring Placentia Bay.

While we hope to shed more light regionally and to provide a useful contribution to the broader field of coastally trapped iKW, this study is not without significant limitations. Perhaps the most important of all is on its use of a simplified model with absence of a realistic bathymetry. As such, we may respond to the original hypothesis of iKW dynamics but fall short in reproducing the more comprehensive motions of CTWs. The effect of the bay's shape, and the reflection in its large (but complex in shape) head in particular, would also benefit from further investigations to better understand the propagation of the waves and their changes in wavelength and amplitude. Simplifications in the model setup with its absence of air-sea and shelf exchanges, notably, preclude the use of the model for long period of time (e.g., seasonal scale). In this study, we found that the model could reasonably be run over a period of 20 days but that finding a state of rest to initialize the model over such period of time could be difficult, especially during the fall, when wind forcing is nearly continuous. Estuarine and mean circulation (e.g., influenced by the shelf), which are of importance when considering water renewals, could also not be assessed via this study and the results of this model.

Nevertheless, the good performance of the model in reproducing the observations, unfiltered from the effects of the processes mentioned above and ignored by the model, indicates the dominance of iKW and the potential for the model results to be used for further studies such as for fisheries and aquaculture-environment interactions. In particular, studies of crustacean larvae (e.g., lobster), sea-lice and viruses dispersion affecting aquaculture activities, which are all of economic importance regionally as well as of dissolved oxygen availability, which depends on water temperature and which recently resulted in significant farmed fish losses (Fisheries and Marine Institute of Memorial University of Newfoundland, 2020) would greatly benefit from the use of such results. Issues related to organic loading from aquaculture farms, however, would certainly need a further development of the model including bathymetry features to be reasonably realistic. Nevertheless, and until the availability of a more realistic model, those results could still help provide with some first estimates.

## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

Observations data used in this manuscript are available in Donnet and Lazure (2020) and in Donnet and Lazure (2021). Model input and output generated through this study as well as illustrations and associated codes are available in Donnet and Lazure (2023). All of those under are licensed under Creative Common Attribution 4.0 International (CC BY 4.0). All the analysis was done under MathWorks MATLAB environment (version 8.6, 2015b). Analyses of the model results used some of the tools provided by Pierre Cazenave's fvcom-toolbox v20180201 (Cazenave, 2018). Normal mode analysis was done using Klink's dynmodes code (Klinck, 1999). Colormaps used that of MATLAB's cmoceans v1.5 toolbox (Greene, 2018; Thyng et al., 2016) and Kristján Jónasson's rgb tool (Jonasson, 2025). Cross-correlations were done using Norbert Marwan's corrgram code
(Marwan, 2025). The numerical model code used in this study (FVCOM v4.1) is available upon request from contacts at https://www.fvcom.org/ with newer versions now available at https://github.com/FVCOM-GitHub/FVCOM.

Acknowledgments

This research was supported by the
Aquaculture Collaborative Research and
Development Program
(project 15-1-N-02). It was enabled in part
by support provided by ACENET (https://
www.ace-net.ca/), BC DRI Group and the
Digital Research Alliance of Canada
(alliancecan.ca). SD would also like to
thank Adam Drozdowski for his helpful
discussions, his help in sourcing ECCC's
HRDPS model data and help in trying to
implement a more realistic bathymetry.
We also thank Ken Hughes and an
anonymous reviewer for their insightful
reviews which significantly improved the
manuscript.

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