Intensification of submesoscale frontogenesis and forward energy cascade driven by upper-ocean convergent flows

Domain: earth_science
Published: 2024-10-25
Editorial outcome: major_revision

Abstract
Upper-ocean fronts are an important component of the global climate system, regulating both the oceanic energy cycle and material transports. In the common paradigm, upper-ocean fronts are generated by frontogenesis at the mesoscale (20–300 km), driven predominantly by confluent horizontal flows initiated by a background straining field. However, the mechanisms by which this frontogenesis extends down to and influences the submesoscale (0.2–20 km), which dominates vertical transports in the ocean, are still understudied. Here, we provide direct observational evidence that submesoscale frontogenesis, defined as the rate at which submesoscale buoyancy gradients intensify, is closely linked to convergent flows. Analysis of year-long measurements by a mooring array in the North Atlantic indicates that both the upper-ocean frontogenetic rate and the horizontal convergence exhibit strong seasonality and scale dependence, with larger magnitudes in winter and at smaller horizontal scales (down to at least 2 km). The frontogenetic rate is found to correlate more strongly with horizontal convergence as the scale decreases, suggesting that convergent flows are the main driver of submesoscale frontogenesis. Crucially, a rapid forward cascade of kinetic energy and enhanced vertical velocities preferentially occur during periods of submesoscale frontogenesis. Our findings highlight a mechanism underpinning the key role of submesoscale fronts in the oceanic kinetic energy cascade and as a focus of vertical transports, and call for a parameterization of such effects in climate-scale ocean models.

Introduction
Density fronts are ubiquitous features in the global ocean, and act as a key mediator for the exchange of climatically-important properties, such as heat and carbon dioxide, between the upper ocean and the atmosphere1–3. Yet, despite the fronts’ significant climatic role, the current generation of climate-scale ocean models cannot adequately represent the lifecycle of fronts, due to the models’ overly coarse resolution and the underdeveloped state of parameterizations of frontal processes.

The mechanism leading to frontal formation is known as frontogenesis, and it can occur in the ocean across a breadth of scales extending from tens of kilometers to a few hundreds of meters4. At the mesoscales (horizontal scales of 20–300 km, periods of weeks-months), the classical deformation frontogenesis model of Hoskins and Bretherton (1972)5 is thought to apply, and describes a scenario in which a confluent strain field near the ocean surface leads to the sharpening of pre-existing density contrasts. Despite this two-dimensional deformation framework’s many successes at rationalizing frontal dynamics in the atmosphere and ocean6–8, more recent theoretical and modeling studies have provided insights into the extension of frontogenesis down to the oceanic submesoscale range (horizontal scales of 0.2–20 km, periods of hours-days). These studies postulate a significant role for the ageostrophic circulations in the upper ocean that result from mixed-layer instabilities9 and boundary layer turbulence10.

The convergence of the horizontal velocity field, referred to as horizontal convergence (i.e. negative horizontal divergence), can drive frontogenesis, as initially demonstrated in earlier theories of dynamic meteorology5,11,12. For oceanic fronts, Barkan et al. (2019)13 derived an asymptotic model to illustrate that near-surface convergent flows can determine gradient sharpening rates in the submesoscale range. They demonstrated that, for anisotropic fronts and filaments that are typically characterized by O(1) Rossby numbers14, a straightforward relationship emerges: the rate of frontal sharpening is equal to the magnitude of horizontal convergence. This correspondence offers predictive capabilities for the growth of vorticity, divergence, and buoyancy gradients. The theory posits that the presence of horizontal convergence at the frontal zone invariably leads to super-exponential growth, a principle that extends beyond two-dimensional models to encompass three-dimensional complexities. Our observational findings in this study are consistent with this theoretical framework, and thus suggest a central role of horizontal convergence in determining the frontogenetic processes in the submesoscale range (i.e. submesoscale frontogenesis).

Submesoscale fronts, which form through submesoscale frontogenesis, are particularly effective at inducing intense vertical velocities in the upper ocean, with submesoscale vertical velocities of O(100 m day−1) typically being an order of magnitude larger than mesoscale vertical velocities of O(10 m day−1)15,16. Convergent vertical motions at submesoscale fronts can effectively concentrate surface materials, and subsequently inject them into the ocean interior17–19.

Another important aspect of the submesoscale frontogenetic process is its driving of intense ageostrophic secondary circulations that lead to a front-focused forward kinetic energy cascade. While some forward energy transfer can occur locally under mesoscale strain-induced frontogenesis, only in the submesoscale frontogenesis scenario it becomes significant and occurs at a rate that is proportional to the frontal convergence20. Given the ubiquity of fronts, submesoscale frontogenesis may thus represent an important sink within the ocean’s energy balance21. This is in contrast to the direct action of mixed-layer and mixed-transitional layer instabilities, which are often shown by submesoscale-permitting simulations to generate near-balanced submesoscale eddies conducive to an inverse energy cascade22–26. Submesoscale frontogenetic processes and fronts are found to be excessively dampened in these submesoscale-permitting simulations27. At any rate, the observational evidence for this emerging view of convergent flow-driven submesoscale frontogenesis is rare28, so that a systematic test with process-targeted measurements is needed.

Here, we aim to provide such test by investigating the mechanism of submesoscale frontogenesis, its associated cross-scale energy cascade, and its dynamical context, in a typical mid-latitude ocean region. With this goal in mind, we analyze a unique suite of in situ observations acquired by a nested mooring array over a full annual cycle (see “OSMOSIS data and processing” in Methods and Supplementary Fig. 1). Our results are in good agreement with the recent theoretical characterizations of submesoscale frontogenesis described above, in that they reveal that: (i) frontogenesis is enhanced in the submesoscale range; (ii) it is underpinned by convergent upper-ocean flows; and (iii) it is associated with a rapid forward kinetic energy cascade toward dissipative scales.

Results
An observed submesoscale frontogenesis event
The occurrence of submesoscale frontogenesis and its associated downscale kinetic energy transfer in our study area is initially illustrated by focusing on a specific wintertime event (Fig. 1). Images of altimetric sea surface height anomaly and high-resolution sea surface temperature show that the mooring array was positioned on the cold (cyclonic) side of a front on 7 February 2013 (Fig. 1a, b). The sea surface temperature changed by >1 °C over a few kilometers at the edge of the front.

During this time, the mooring array measured the upper ocean to be weakly stratified, with the mixed layer deepening rapidly from 200 m down to >300 m and then shoaling to about 150 m within 1 day (Fig. 1c). The measured kinetic energy was greatly elevated and surface-intensified during the mixed layer deepening (Fig. 1d), corresponding to a maximum horizontal velocity of about 0.38 m s−1. The enhanced kinetic energy in the mixed layer was concurrent with predominantly positive frontogenetic rate (Tb > 0) and horizontal convergence (−δ > 0), reaching respective maximum values of 0.59f and 0.76f, where f is the Coriolis parameter (Fig. 1e, f).

Persistent upper-ocean horizontal convergence implies downwelling in underlying layers. Vertical velocity was directly estimated using the non-diffusive density equation29, and intense downwelling of order −100 m day−1 was indeed seen below the mixed-layer base during this frontogenetic event (Fig. 1g). Lastly, the rate of cross-scale kinetic energy transfer was quantified by applying the coarse-graining approach to the mooring data27,30–32. An enhanced forward energy cascade, at a rate of about 10−7 m2 s−3, was found, which is an order of magnitude larger than the winter-mean energy transfer rate (Fig. 1h; also see Supplementary Fig. 2). This event is analogous to that reported by D’Asaro et al. (2018)28, in which rapid horizontal convergence of a large number of surface drifters was observed on the dense side of a front in the northern Gulf of Mexico, accompanied by strong sinking of water at the front.

Features of submesoscale turbulence over an annual cycle
The success of the mooring array in quantifying the frontogenetic event described above motivates us to explore the mechanism and effects of submesoscale frontogenesis over the entire year of observations. To begin with, we examine the degree to which subinertial flows depart from geostrophic balance, which is a measure of the importance of ageostrophic motions. A 24 h low-pass filter is applied to mooring velocity and density measurements to remove variability in the internal wave band (see “OSMOSIS data and processing” in Methods). Departure from geostrophy can be assessed by comparing the vertical shear of horizontal velocity at the central mooring to the horizontal gradient of buoyancy across horizontal scales from 18 km–2 km (Fig. 2a–c).

The vertical shear Uz is found to be highly variable and frequently deep-reaching down to 500 m throughout the year, attaining magnitudes of order 10−3 s−1 within and below the mixed layer (Fig. 2d). The horizontal buoyancy gradient |∇h b| generally follows the vertical shear closely over the annual cycle, but exhibits a dependence on horizontal scale (Fig. 2e). Notably, the horizontal buoyancy gradient magnitude at 2 km is considerably larger than those at 9 km and 18 km, with respective winter root-mean-square (RMS) values of 5.5×10−8, 3.5×10−8 and 2.6×10−8 s−2. This indicates the increased sharpening of fronts in the submesoscale range. At the 2-km scale, the daily-averaged magnitude of the horizontal buoyancy gradient term |∇h b|/f is systematically larger than that of the vertical shear term Uz in the thermal wind balance equation (Supplementary Fig. 3). This denotes that the observed upper-ocean subinertial motions at that scale contain a substantial ageostrophic component (i.e. ageostrophic flows not associated with internal waves). The concurrent occurrence of sharper horizontal buoyancy gradients and stronger ageostrophic motions at the 2 km scale points to a common underpinning by submesoscale frontogenesis.

A window into the dynamics of submesoscale frontogenesis is provided by comparing the normalized frontogenetic rate Tb/f, horizontal convergence −δ/f and relative vorticity ζ/f across the 18 km, 9 km and 2 km horizontal scales sampled by the mooring array (see “Kinematic properties” in Methods). All variables consistently display pronounced seasonality and scale dependence, with larger amplitudes in winter and at smaller scales (Fig. 3a–c). The quantities diagnosed at 2 km scales are more surface-intensified, with RMS values of Tb/f and −δ/f peaking at 0.3, and those of ζ/f approaching 0.5 near the surface. The comparable magnitudes of −δ/f and ζ/f at 2 km scales indicate that horizontally convergent flows play an increasingly important dynamical role at smaller scales, consistent with a progressive breakdown in geostrophic balance. In contrast, the RMS values of all variables at 9 km and 18 km have magnitudes of order 0.1, approximately a factor of 4 smaller than those at 2 km.

A positive skewness in frontogenetic rate, horizontal convergence, and relative vorticity at 2 km scales is observed only in winter (Fig. 3d–f). Such skewness values are consistent with previous modeling and observational studies of submesoscale turbulence33–37. Frontogenetic rate and horizontal convergence are positively skewed above 200 m, while the skewness of vorticity extends down to below 450 m, with skewness decreasing gradually from 1.5 at 50 m to <0.5 below 200 m. These asymmetric distributions indicate that active submesoscale turbulence is at play in the wintertime upper ocean, with more extensive occurrence of frontogenetic processes, horizontal convergence, and cyclonic vorticity there. The positive skewness in upper-ocean layers illustrates our study area’s generic propensity to host submesoscale frontogenesis. By contrast, no skewness features are seen at larger scales or in summer. Overall, these diagnostics indicate that nonlinear ageostrophic dynamics are increasingly important for frontogenetic processes, down to the sampled scales of O(1 km).

Submesoscale frontogenesis induces a forward energy cascade
To substantiate our demonstration of the central involvement of convergent flows in submesoscale frontogenesis, we construct scatterplots of daily-averaged horizontal convergence −δ/f versus frontogenetic rate Tb/f at horizontal scales of 18 km, 9 km and 2 km (Fig. 4). At 2 km scales, −δ/f and Tb/f are strongly correlated, with a correlation coefficient R2 of ~0.78 (p < 0.01), and closely follow a one-to-one relationship as predicted by the theory of Barkan et al. (2019)13. However, this correlation between −δ/f and Tb/f is also scale-dependent. As the resolved horizontal scales decrease, the correlation coefficient R2 between −δ/f and Tb/f reduces to ~0.3 (p < 0.01) at 9 km scales and 0.11 (p > 0.05) at 18 km scales. In contrast to horizontal convergence, neither relative vorticity ζ/f nor strain rate α/f are significantly correlated with Tb/f at any scale, with correlation coefficients R2 almost always < 0.2 and p-values exceeding 0.05 across all resolved scales (Supplementary Fig. 4). This further suggests that the strong convergent flows—and not strain—are most likely the main factor in governing submesoscale frontogenesis.

We further explore the effects of submesoscale frontogenesis on the cross-scale kinetic energy transfer, by applying the filter-based coarse-graining framework to compute energy fluxes across temporal scales (see “Kinetic energy transfer” in Methods). The rates of energy transfer for a filter scale of 2 days (Π2 ω d, representing the horizontal kinetic energy transfer from flows with temporal scales > 2 days to those with shorter periods) during frontal and non-frontal periods in winter are compared in Fig. 5a. Here, oceanic fronts are defined as the ninetieth percentile of the horizontal convergence (|δ|2d > 0.3, where δ2d is the divergence smoothed over the same 2-day scale for consistency; frontal periods are shown in Fig. 2d). Similar results are found when considering a lateral buoyancy gradient threshold for defining fronts, and when using a longer or shorter period for computing cross-scale kinetic energy transfer rate (Supplementary Figs. 5–6). The 2 day period corresponds to a horizontal scale of ~8 km, where this scale was determined via a frequency-resolved structure function analysis38. This horizontal scale is in line with the transition scale of 6–10 km for a change to increasingly nonlinear ageostrophic dynamics in the California Current System, identified using a cross-spectral phase approach39.

Both front-averaged and winter-averaged energy transfers are positive in the upper ocean, that is, directed from temporal scales > 2 days toward shorter scales (i.e. a forward transfer). The front-averaged forward transfer is two times larger than the winter-averaged flux, indicating that the energy flux across the 2 day scale is concentrated at fronts. The horizontal convergence (|δ|2d) and the kinetic energy at scales < 2 days (KE02d) are also enhanced at fronts relative to the winter averages (Fig. 5b, c). We also find a near-linear scaling between Π2 ω d and |δ|2d KE02d (Fig. 5d), consistent with the numerical investigation of Srinivasan et al. (2023)20. Further, the diagnosed vertical velocity at fronts, with RMS value exceeding 70 m day−1, is substantially larger than the RMS value of vertical velocity during the entire winter (Fig. 5e and see “Vertical velocity” in Methods). In conclusion, all of the key predictions of the emergent view of submesoscale frontogenesis as a horizontal convergence-linked mechanism stand to our observational test.

Methods
OSMOSIS data and processing
The data analyzed in this study were primarily collected from a mooring array deployed over the Porcupine Abyssal Plain (48.63°–48.75° N, 16.09°–16.27° W) in the northeast Atlantic (Fig. 1a), as part of the Ocean Surface Mixing, Ocean Submesoscale Interaction Study (OSMOSIS) experiment27,29,59. Nine sub-surface moorings were deployed for the period September 2012—September 2013, arranged in two concentric quadrilaterals with side lengths of ~13 km (outer cluster) and 1–2 km (inner cluster) around a centrally located single mooring. Importantly, this configuration enabled simultaneous measurements of meso- and submesoscale properties. The observational site lies at the eastern edge of the North Atlantic gyre, a region of weak mean flow and moderate eddy kinetic energy that is arguably representative of a substantial fraction of the global ocean. Internal wave energy levels are also moderate and primarily contributed by semi-diurnal internal tides, near-inertial waves, and the internal wave continuum60,61.

Mooring sensors comprised a series of paired MicroCAT conductivity-temperature-depth (CTD) sensors and acoustic current meters at different depths, spanning the approximate depth interval 30–530 m (Supplementary Fig. 1). Temperature, salinity and horizontal velocity measured by CTD and current meter instruments, with respective sampling intervals of 5 and 10 min, were interpolated onto a uniform depth grid (10 m intervals between depths of 50 m and 520 m) and averaged onto hourly intervals. A fourth-order low-pass Butterworth filter with a cut-off of 24 h (one inertial period is ~16 h) was then applied to the hourly data to remove unbalanced super-inertial motions. Note that internal diurnal tides cannot be generated nor propagate into the study region, and that barotropic diurnal tides are rather weak27,29. Further, the mooring measurements were complemented by hydrographic observations acquired by two ocean gliders that navigated in a bow-tie pattern across the mooring array for the entire sampling period46. The mixed-layer depth is calculated from coincident glider data using a threshold value of potential density increase (Δρ = 0.03 kg m−3) from a near-surface value at 10 m62.

Kinematic properties
Horizontal divergence, the vertical component of the relative vorticity, and strain rate can be calculated using spatial derivatives of velocity,
δ = ∇h · u = ∂u/∂x + ∂v/∂y, ζ = k · ∇ × u = ∂v/∂x − ∂u/∂y, α = √((∂u/∂x − ∂v/∂y)2 + (∂v/∂x + ∂u/∂y)2),
where k is the vertical unit vector, ∇h is the spatial gradient operator, u = (u,v,w) is the 3d velocity vector, the h subscript denotes horizontal component, and b = g(1 − ρ/ρ0) is buoyancy (with g denoting the gravitational acceleration, ρ the potential density, and ρ0 = 1025 kg m−3 the reference density).

The focus of this study is to examine the key factors in setting submesoscale frontogenesis and the associated energy transfers from the mooring observations. To this end, we quantify the rate of frontal sharpening using the frontogenetic rate13, defined as
Tb = Fs = |∇h b|2, (1)
where the frontogenesis function is Fs = Q · ∇h b, with Q = (-(∂u/∂x)(∂b/∂x) − (∂v/∂x)(∂b/∂y), -(∂u/∂y)(∂b/∂x) − (∂v/∂y)(∂b/∂y)) denoting the so-called Q vector12.

The type of spatial arrangement used for the OSMOSIS array is rare in mooring deployments36,63,64, and makes this dataset particularly well suited for quantifying the horizontal gradients of horizontal velocity and buoyancy (Fig. 2a–c). In this study, the analysis is performed using the full expanse of the mooring array (18 km) and mooring triplets (9 km and 2 km) to estimate the horizontal derivatives in velocity and buoyancy. The velocity and buoyancy measurements are taken at three corners for each triangle area, and then the horizontal derivatives can be calculated using the divergence theorem and the line integral around the triangle boundary. The water column in the shallow pycnocline during non-winter months exhibits super- and sub-inertial heaving, which produces overly large horizontal buoyancy gradients46; such signals are excluded here. All variables are normalized by the local Coriolis parameter f = 2Ω sin ϕ, where Ω is the Earth’s angular velocity and ϕ the latitude.

Kinetic energy transfer
Our approach to quantifying cross-scale horizontal kinetic energy transfer, which refers to the exchange of kinetic energy across different flow scales, is based on the “coarse-graining” framework30,31. This technique involves calculating both the magnitude and direction (upscale or downscale) of nonlinear energy exchange from the quadratic terms in the equations of motion. This method is advantageous in comparison to the traditional spectral methods because it does not require windowing, nor the assumptions of homogeneity or isotropy65. Moreover, because the framework is Galilean invariant and employs filters in physical space, it can also provide structural information about the flow features where energy transfers occur. We define the energy transfer, Π ω, as
Π ω(t) = (∇h u hω + ∇h u hω T) : ((u h u h) ω − u hω u hω), (2)
where t is time, u h denotes the vector of the total horizontal velocity, and u hω is the horizontal velocity component for frequencies lower (i.e. longer timescales) than a given value of ω, ∇h is a horizontal gradient, the superscript T denotes a transpose operator, and the colon is a tensor inner product. The result is a scalar that indicates the direction of energy transfer, with positive (negative) values denoting transfers to higher (lower) frequency.

From a mathematical perspective, the coarse-graining approach can be equivalently applied in both the wavenumber and frequency domains, as demonstrated by Naveira Garabato et al. (2022)27 and Srinivasan et al. (2023)20. One advantage of applying the coarse-graining approach in the frequency domain is that balanced submesoscale motions can be separated from unbalanced internal waves, whereas they are practically indistinguishable in the spatial domain.

Vertical velocity
The density conservation equation is used to determine vertical velocity, neglecting the diffusion term29,
Dρ/Dt = ∂ρ/∂t + u ∂ρ/∂x + v ∂ρ/∂y + w ∂ρ/∂z = 0, (3)
where D/Dt is the material derivative. The vertical velocity is estimated from the sum of a local isopycnal displacement term and a horizontal advection term, by rearranging equation (3) as
w = −(∂ρ/∂t + u ∂ρ/∂x + v ∂ρ/∂y) / (∂ρ/∂z). (4)

Vertical velocity in the mixed layer is not derived from the density conservation equation, as the neglected diffusion term becomes significant there. An alternative method for estimating vertical velocity is to apply the continuity equation under the assumption of zero vertical motion at the sea surface. However, measurements within the top 50 m were not conducted. To effectively apply the continuity equation, we would need detailed knowledge of the vertical distribution of horizontal divergence, or assume depth independence of horizontal divergence in the top 50 m. This assumption, however, is likely invalid according to Tarry et al. (2022)37.

Observational uncertainty in the horizontal divergence
We assess the uncertainties in the horizontal divergence diagnostics by addressing two main sources of error: mooring motion and instrumental inaccuracies in velocity measurements. First, the horizontal divergence estimates are based on horizontal gradients derived from velocity data collected by moorings. However, any undetected motion of the moorings can lead to uncertainty in the precise measurement of locations. Stochastic models indicate that these horizontal displacements are typically < 500 m59. To incorporate this uncertainty, we model inter-mooring distance perturbations associated with mooring motion using time integration of a Gaussian white noise process with zero mean and non-zero variance, estimated from differential horizontal currents59. Second, there is instrumental error due to the limited precision of the sensors used in the moorings, which is an inherent constraint in the data collection process. According to the manufacturer’s specifications, Nortek Aquadopp current meters have an accuracy of 5 × 10−3 m s−1.

To quantify the total uncertainty arising from these two factors, we introduce random errors from both sources simultaneously and allow them to accumulate in the horizontal divergence estimates. We assume that the errors from mooring movement and instrumental noise are independent of each other. This procedure is repeated 10,000 times. Supplementary Fig. 7 illustrates the results, showing that the observational uncertainties considered here have only a minor impact. The horizontal divergence diagnostics remain qualitatively unchanged, while the quantitative effects of these uncertainties typically result in perturbations of < 0.025f, or ~10%.

Lastly, the vertical resolution of the velocity measurements is limited, and varies among different mooring clusters. The central mooring is the most heavily instrumented, with 13 current meters, while the inner and outer moorings have seven and five current meters, respectively. To assess the uncertainty arising from varying vertical resolution, we calculated the horizontal divergence using vertically sub-sampled horizontal velocity data. Specifically, we reduced the vertical resolution of the central mooring by selecting seven and five current meters at approximately the same depths as those on the inner and outer moorings, corresponding to estimates at 2 km and 9 km, respectively. We found that our diagnostics are weakly sensitive to the vertical resolution of the data (Supplementary Fig. 8).

Statistical significance of the cross-scale kinetic energy transfer diagnostics
To determine the statistical significance of the diagnosed Π ω from the observations, we conduct kinetic energy transfer calculations using synthetic horizontal velocity time series. These synthetic time series replicate the amplitudes of the observations but have randomized phases27. As a result, these synthetic time series are expected to exhibit, on average, no kinetic energy transfer, meaning that any non-zero transfers identified can be attributed to limited sampling. We treat this zero-transfer scenario as the null hypothesis and test the significance level at which it can be rejected using the actual time series data. Specifically, we evaluate the averaged kinetic energy transfer at fronts over the winter period. The observed values exceed the upper limit of the confidence interval across nearly the entire depth range, suggesting that the null hypothesis can be rejected with ~95% confidence (Supplementary Fig. 9). Consequently, we conclude that the downscale kinetic energy transfer diagnosed at fronts during winter is statistically significant.

Data availability
All OSMOSIS mooring data are freely available, and are archived at the British Oceanographic Data Centre. Moored observations are accessible at https://www.bodc.ac.uk/data/bodc_database/nodb/data_collection/6093/ with platform as “Subsurface mooring”. AVISO sea level anomaly and surface geostrophic velocity data are available at https://data.marine.copernicus.eu/products. VIIRS data can be obtained from NOAA Comprehensive Large Array-Data Stewardship System (https://www.aev.class.noaa.gov/saa/products/welcome). The LLC4320 simulation output is available at https://data.nas.nasa.gov/ecco/data.php. Source data to reproduce the figures of this paper are deposited in the Zenodo repository under https://doi.org/10.5281/zenodo.13918954.

Code availability
The codes used for generating the figures of this paper are available at https://doi.org/10.5281/zenodo.13918954.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Comments on Yu et al. (2024) submitted to Nature Communications\nGeneral comments\nIn this manuscript, the authors examined submesoscale frontogenesis and the associated forward energy cascade in the\nupper ocean through analyzing observation data from the OSMOSIS mooring array. The authors found that submesoscale\nfrontogenesis is mainly driven by the convergent flows, which is more efficient than the classical mesoscale strain-induced\nfrontogenesis. They also suggested that the convergent flows-induced by submesoscale frontogenesis can generate rapid\nforward cascade of kinetic energy. The main novelty of this manuscript is that the authors have provided direct observational\nevidences of the two important scientific issues mentioned above, although the relevant\nviewpoints were already shown by\nprevious theoretical and simulation studies. Overall, I think this paper is suitable to be published in Nature Communications\nbut the following major and minor issues have to be addressed.\nMajor comments\n1.One of my main concern is the method to calculate kinetic energy transfer in the frequency domain. The kinetic energy\ncascade is traditionally calculated in the perspective of wave numbers. Although the paper by Naveira Garabato et al. (2022,\nJPO) extended the coarse-graining method to frequency domain to calculate kinetic energy\ntransfer, it is difficult to infer the\nprecise spatial scale to explain the calculated results. Here, the authors used a filter scale of 2 days to perform the\ncalculation and argued that this period falls into the submesoscale (spatial scale of ~8 km). However, in addition to\nsubmesoscales, many waves such as diurnal tides and near-inertial waves also have time scales shorter than 2 days but\ntheir spatial scales are much larger than 10 km.\n2.I also have a concern about the robustness of the calculated kinetic energy transfer. According to previous high-resolution\nsimulations-based studies, we know that the kinetic energy transfer associated with submesoscales varies significantly both\nspatially and temporally. We can obtain a robust kinetic energy transfer only after making average over a larger spatial\ndomain and a longer time period. Actually, even in the paper of Naveira Garabato et al. (2022, JPO), the authors have\nacknowledged that the calculated kinetic energy transfers “have marginal statistical significance and should be regarded\ncautiously”. So, more analysis is needed to demonstrate the robustness or statistical significance of the calculated results\nhere.\n3.Robustness of the calculated horizontal divergence should also be demonstrated. The horizontal divergence is a small\nresidue of two larger terms (typically with opposite signs) and it is quite sensitive to the measuring errors of horizontal\nvelocities. Given that the current meters have coarse vertical resolutions and that they were on different vertical locations for\ndifferent moorings, the authors chose to interpolate the measured velocities onto 10-m uniform depth grid. Therefore, in\naddition to the measuring errors of the current meters themselves, the vertical interpolation may also result in large errors in\nthe calculated horizontal divergence. The calculated errors may become even larger when the moorings have large swings\nor tilt under the influence of strong currents. Here, I suggest adding more analysis about the errors of the calculated\nhorizontal divergence. To this end, you should show the depth-time plot of the horizontal divergence during the\nobservational period or at least during the winter season.\n4.Mechanisms of the main findings of this study should be clarified. Firstly, the authors suggested the importance of\nconvergence in the submesoscale frontogenesis but did not show the mechanisms accounting for the convergent flows. Are\nthey associated with unbalanced wave motions, Ekman currents, turbulent mixing, or other higher-order balanced motions?\nSecondly, the authors suggested that the convergent flows can further induce rapid forward energy cascade but the\nmechanisms of the forward energy cascade was not discussed. Are the forward energy cascade associated with somewhat\nfrontal instabilities or interactions between balanced motions and internal waves? I hope the authors can add more analysis\nto clarify the relevant mechanisms.\nMinor comments\n1.Line 13: “remain unclear due to a lack of observations”. This statement is too strong because earlier theoretical and\nsimulation studies have already pointed out the relevant mechanisms or routes.\n2.Line 22: Submesoscales are not always an oceanic energy sink it may also be an energy source for mesoscales through\ninverse energy cascade.\n3.Lines 44-48: The earlier theories of dynamic meteorology have already shown the role of convergent flows in the\nfrontogenesis. You should also cite the much earlier references here.\n4.Lines 59-63: Many recent studies based on high-resolution simulations have found that the energy cascade in the\nsubmesoscale range is dominated by inverse energy cascade (e.g., Ajayi et al., 2021, JAMES; Zhang et al., 2023, NC). Is\nthis because the resolution of their simulations is not enough to resolve the submesoscle frontogenesis ? The authors\nhighlight the importance of submesoscle frontogenesis in forward energy cascade here, but the mesoscale strain-induced\nfrontogenesis may also play a similar role.\n5.Line 92 and Fig. 1h: Just based on result in one-day period, it is difficult to infer whether the forward energy cascade is\nenhanced. I suggest extending the results in Figures 1c-h to one week to highlight the enhancement of forward energy\ncascade on the day shown here.\n6.Lines 112-113 and 240-241: The 16-hour low-pass filter (one inertial period) was used to obtain the sub-inertial motions.\nThe obtained results actually also contain signals of some remaining near-inertial waves (frequency of 0.8f-1.2f) and also\ndiurnal tidal waves. In order to totally remove the near-inertial waves and tidal signals, you’d better use 24-hour low-pass\nfilter.\n7.Lines 127-129: You may cite more observational studies that support the skewness of submesoscale turbulence.\n8.Lines 158-160: In addition to the results during frontal events in Figures S4 and S6, I suggest also showing the entire\nresults using another supplementary figure (with frontal events being marked using lines). By comparing the results during\nthe periods with fronts and without fronts will help highlight the role of fronts.\n9.Lines 200-202: What is the mechanism causing the strong convergence? Is it due to the remaining near-inertial waves?\nPlease also refer to my 4th major comment and 6th minor comment.\n10.Lines 203-205: Given that the fronts generated by convergent flows-induced submesoscale frontogenesis are usually\nvery narrow (with very short length scale), their vertical scale or influence depth may also be small. So, their role in\ncontacting the mixed layer and deeper ocean may also be limited compared with the submesoscales with larger spatial\nscales.\n11.Lines 212-216: Do the remaining near-inertial internal waves play a role in the forward energy cascade? Please also\nrefer to my 4th major comment and 6th minor comment.\n12.Lines 261-263: There are also other meso- to submesocale resolving mooring arrays that can certainly quantify the\nhorizontal gradients of horizontal velocity and buoyancy (such as those deployed in the northwestern Pacific and South\nChina Sea). I think you should not ignore them here.\n13.Lines 285-293: Based on the density conservation equation, you can not obtain the vertical velocity within the mixed\nlayer. How about using the continuity equation to calculate the vertical velocity? If the calculated horizontal divergence is\nrobust, you may do so by assuming zero vertical velocity at sea surface.", "reviewer_2": "This paper presents compelling observational evidence of submesoscale frontogenesis driven by horizontally-convergent\nstrain flow. The data is consistent with previous theoretical work from Barkan et al. 2019. This is an important finding\nbecause the convergence-dominated frontogenesis events are likely unresolved in most ocean models. The strong,\nlocalized convergence also has significant implications for vertical subduction and accumulation of buoyant material at\nfronts. I would recommend publication in Nature Communication after some minor revisions which are described\nbelow.\nThe introduction largely focuses on the theoretical aspects of frontogenesis and energy transfers. Personally, I would have\nspent more time motivating the paper by discussing the importance of the large vertical velocities and horizontal\nconvergence that is observed at the submesocale fronts. In my view, this angle would provide a broader motivation.\nDespite their centrality to the paper, submesoscale fronts and submesoscale frontogenesis aren’t clearly defined in the\npaper. Submesocales are defined as having a scale less than 10km. This is ambiguous for a front where the along-front and\ncross-front lengthscales can be very different. I also don’t think that the scale is the most relevant measure. For example, it\nwould be possible for a large-scale quasi-balanced flow to slowly deform a front so that the front remained well-\napproximated by QG or SG theory well beyond the point where the cross front scale is less than 10km. I would suggest that\nthe authors should define a submesoscale front as one which is generated through frontogenesis by submesoscale motions.\nIn any event, these terms should be carefully defined.\nThere have been several papers which have presented submesoscale and frontal statistics from the OSMOSIS site where\nthe measurements were collected. Although I realize that space is limited in this journal, it would be helpful to briefly review\nthis work and discuss how this papers fits amongst those findings.\nminor comments:\nline 48: what does “tightly” refer to in this context?\nline 99: “eliciting” doesn’t seem like the right word.\nline 108: “This manifests” doesn’t sound right in this context\nline 113: Why does this imply that the flow is not associated with internal waves?\nline 126: The wording needs to be improved here\nline 148: typo: “train”"}, "author_response": "Response to Reviews:\nWe are grateful to the two Reviewers for their very helpful and constructive comments. In\nthe following, we outline how we have responded to the comments by the Reviewers. In\neach case, the Reviewers’ comments are shown in blue, and our responses in black. All\nline numbers in our replies refer to the revised version of the manuscript with tracked\nchanges.\nResponse to Reviewer 1\nGeneral comments\nIn this manuscript, the authors examined submesoscale frontogenesis and the associated\nforward energy cascade in the upper ocean through analyzing observation data from the\nOSMOSIS mooring array. The authors found that submesoscale frontogenesis is mainly\ndriven by the convergent flows, which is more efficient than the classical mesoscale\nstrain-induced frontogenesis. They also suggested that the convergent flows-induced by\nsubmesoscale frontogenesis can generate rapid forward cascade of kinetic energy. The\nmain novelty of this manuscript is that the authors have provided direct observational\nevidences of the two important scientific issues mentioned above, although the relevant\nviewpoints were already shown by previous theoretical and simulation studies. Overall, I\nthink this paper is suitable to be published in Nature Communications but the following\nmajor and minor issues have to be addressed.\nWe thank the Reviewer for appreciating the value of our work, and for their advice on how\nto corroborate and strengthen our key results. We took into account all their suggestions\nand hope this leads to a significant improvement of the paper.\nMajor comments\n1.One of my main concern is the method to calculate kinetic energy transfer in the\nfrequency domain. The kinetic energy cascade is traditionally calculated in the\nperspective of wave numbers. Although the paper by Naveira Garabato et al. (2022, JPO)\nextended the coarse-graining method to frequency domain to calculate kinetic energy\ntransfer, it is difficult to infer the precise spatial scale to explain the calculated results.\nHere, the authors used a filter scale of 2 days to perform the calculation and argued that\nthis period falls into the submesoscale (spatial scale of ~8 km). However, in addition to\nsubmesoscales, many waves such as diurnal tides and near-inertial waves also have time\nscales shorter than 2 days but their spatial scales are much larger than 10 km.\nThank you for this insightful comment. First, from a mathematical perspective, the coarse-\ngraining method can be applied indistinctively in the spatial or temporal domains. This\npoint is discussed and explicitly demonstrated by Barkan et al. (2017) in their investigation\nof eddy-internal wave kinetic energy (KE) exchanges in idealised simulations (see in\nparticular their Appendix B and section 5). Also, Naveira Garabato et al. (2022) and\nSrinivasan et al. (2023) showed the comparison of KE transfers across temporal and\nspatial scales based on realistic and idealised simulations, respectively (see Figures R1-\nR2 below). Results from both studies have demonstrated a similar pattern of KE transfers,\nthat is, an inverse energy cascade at larger temporal or spatial scales, and a forward\nenergy cascade at smaller temporal or spatial scales.\nSecond, frequency and horizontal wavenumber spectra of sub-inertial (i.e. with\nfrequencies lower than the inertial frequency (cid:1)) KE in the ocean are characteristically red.\nKE increases quasi-monotonically with decreasing frequency and horizontal wavenumber,\nsuch that slowly evolving eddies are systematically larger than rapidly evolving eddies.\nThis feature of the ocean’s eddy field can be readily illustrated with a 2D (frequency–\nhorizontal wavenumber) spectrum of KE in the LLC4320 simulation of the OSMOSIS area\n(Figure R3a), which reproduces the expected relationship between eddy frequency and\nhorizontal size, and shows that such relationship breaks down for near- and super-inertial\ninternal wave motions (e.g., near-inertial waves and internal tides are characterized by\nhorizontal wavenumbers as small as those of the lowest-frequency sub-inertial eddies).\nThird, the Reviewer is correct in that super-inertial waves may have spatial scales larger\nthan the submesoscale spatial scale of 0.2-20 km. For instance, Callies et al. (2020) and\nYu et al. (2022) both showed the spatial scale of near-inertial waves is larger than 37.4\nkm based on a frequency structure function approach and dispersion relations,\nrespectively. In fact, one advantage of applying the coarse-graining approach in\nfrequency domain analysis is that there is a frequency separation between balanced\nsubmesoscale motions and unbalanced internal waves, whereas they are practically\nindistinguishable in the spatial domain. One last point is that baroclinic diurnal tides\ncannot be generated or propagated at the study region (48.75ºN), and barotropic diurnal\ntides are rather weak, as evidenced by the absence of spectral peaks at diurnal\nfrequencies (see Figure R3b below).\nIn response to the Reviewer’s comment, the validity and advantanges of applying the\ncoarse-graining approach in the frequency domain are now explicitly stated (lines 331-\n335). We have also added several sentences to clarify the characteristics of internal\nwaves in the study region (lines 275-277 and 284-286).\nFigure R1: Time series of the cross-scale KE transfer at the surface in the LLC4320 simulation\ncomputed as a function of (a) time scale and (b) horizontal scale. Mean cross-scale KE transfers\nfor the entire year, winter (December–February) and spring (March–May) are also shown as a\nfunction of (c) time scale and (d) horizontal scale. Figure from Naveira Garabato et al. (2022).\nFigure R2: The curves in are the total horizontal flux Π!\" (black), the deformation shear production\nΠ#\" (red), and the convergence production Π$\" (blue) as a function of frequency (top panel) and\nhorizontal wavenumber (bottom panel) from 500 m (left panel) and 2 km (right panel) model\nresolutions, respectively. Figure from Srinivasan et al. (2023).\nFigure R3: (a) Frequency–horizontal wavenumber spectrum of KE (multiplied by frequency and\nhorizontal wavenumber) at the surface in the OSMOSIS area in the LLC4320 simulation. (b)\nIllustrative frequency spectra of KE at 50 and 500 m in the OSMOSIS mooring observations. Gray\nshading indicates 95% confidence intervals. Significant periods are marked by dashed lines and\nlabelled in both panels. Figure from Naveira Garabato et al. (2022).\n2.I also have a concern about the robustness of the calculated kinetic energy transfer.\nAccording to previous high-resolution simulations-based studies, we know that the kinetic\nenergy transfer associated with submesoscales varies significantly both spatially and\ntemporally. We can obtain a robust kinetic energy transfer only after making average over\na larger spatial domain and a longer time period. Actually, even in the paper of Naveira\nGarabato et al. (2022, JPO), the authors have acknowledged that the calculated kinetic\nenergy transfers “have marginal statistical significance and should be regarded\ncautiously”. So, more analysis is needed to demonstrate the robustness or statistical\nsignificance of the calculated results here.\nThank you for pointing this out. We share the Reviewer’s concern that only a number of\nevents can be captured and analysed here with a yearlong submesoscale-resolving\nmooring array. Nevertheless, it should be highlighted that Naveira Garabato et al. (2022,\nJPO) essentially indicated that the forward energy transfers between mesoscales and\nsubmesoscale (at the temporal scale of 5 days) are robust, while the inverse energy\ntransfers between mesoscales and submesoscale have marginal statistical significance.\nOne thus can expect forward energy transfers at shorter temporal scales (e.g., 2 days in\nthe manuscript) to be stronger and robust. To further confirm this, we followed the\napproach introduced in Appendix C of Naveira Garabato et al. (2022, JPO), and applied\nthe KE transfer calculation to synthetic time series of horizontal velocity that have the\nsame amplitudes as in the observations but randomized phases. The synthetic time\nseries is supposed to have zero KE transfer, and any nonzero estimates are attributed to\nthe limited sampling. Figure R4 shows that the observed forward energy transfer across\n2 days at fronts (orange curve) is substantially larger than the synthetic energy transfer\n(blue curve), indicating that the downscale KE transfer at these fronts is robust. We have\nnow added a new subsection in the Methods to illustrate the robustness of the calculated\nKE transfer (lines 376-387).\nFigure R4: Statistical significance analysis for the KE transfer from time scales longer than 2 days\nto shorter periods, Π% (with positive values indicating a downscale KE transfer). The red curve\nshows the observed winter KE transfer values at fronts, and the blue curve shows the mean\nestimates for a zero-transfer flow with the same amplitude as observed. Shading denotes the\nupper and lower boundaries of the 95% confidence intervals.\n3.Robustness of the calculated horizontal divergence should also be demonstrated. The\nhorizontal divergence is a small residue of two larger terms (typically with opposite signs)\nand it is quite sensitive to the measuring errors of horizontal velocities. Given that the\ncurrent meters have coarse vertical resolutions and that they were on different vertical\nlocations for different moorings, the authors chose to interpolate the measured velocities\nonto 10-m uniform depth grid. Therefore, in addition to the measuring errors of the current\nmeters themselves, the vertical interpolation may also result in large errors in the\ncalculated horizontal divergence. The calculated errors may become even larger when\nthe moorings have large swings or tilt under the influence of strong currents. Here, I\nsuggest adding more analysis about the errors of the calculated horizontal divergence.\nTo this end, you should show the depth-time plot of the horizontal divergence during the\nobservational period or at least during the winter season.\nWe thank the Reviewer for this constructive comment. First, we have examined the\nuncertainties in the horizontal divergence estimates from two sources: mooring motion\nand instrumental errors in the velocity measurements. Mooring motions are estimated\nfrom time-integration of differential horizontal currents, and instrumental errors are\nobtained from manufacturers’ specifications. We introduce random uncertainties from\nthese two sources (with magnitudes described in the revised manuscript) into the\nhorizontal divergence estimates simultaneously, assuming that errors associated with\nmooring motion and instrumental noise are independent. 95% confidence intervals are\nestimated from a Monte Carlo approach by repeating this exercise 10,000 times. We find\nthat the observational uncertainties on horizontal divergence estimates are minor (see\nFigure R5 below). Second, a sensitivity test for vertical resolution is done in the horizontal\ndivergence analysis. By varying vertical resolution of each mooring cluster to re-do the\ncalculation of horizontal divergence, the structure and magnitude vary insignificantly (see\nFigure R6 below). Thus, we note that the horizontal divergence estimates are only weakly\nsensitive to the vertical resolution of our measurements.\nIn response to the Reviewer’s comment, we have included a new subsection in the\nMethods to illustrate the robustness of the calculated horizontal divergence (lines 349-\n375) and a depth-time plot of the horizontal divergence, as suggested by the Reviewer\n(see Figure R8 below or Figure S5 in the supporting information).\nFigure R5. Depth-resolved (a) root-mean-square (RMS) and (b) skewness of the normalised\nhorizontal convergence −(cid:2)/(cid:1) estimated at horizontal scale of 2 km during winter (solid blue curve)\nand summer (dashed blue curve), where uncertainties are caused by instrumental errors and\nmooring motions. Shading denotes 95% confidence intervals estimated from the bootstrap\napproach.\nFigure R6: Comparison of horizontal divergence estimated from two different vertical resolutions\nat spatial scales of (a) 2 km and (b) 9 km. Vertical resolutions of ~35 m, ~65 m and ~95 m\ncorrespond to 13, 7, 5 sensors on the central mooring, respectively.\n4.Mechanisms of the main findings of this study should be clarified. Firstly, the authors\nsuggested the importance of convergence in the submesoscale frontogenesis but did not\nshow the mechanisms accounting for the convergent flows. Are they associated with\nunbalanced wave motions, Ekman currents, turbulent mixing, or other higher-order\nbalanced motions? Secondly, the authors suggested that the convergent flows can further\ninduce rapid forward energy cascade but the mechanisms of the forward energy cascade\nwas not discussed. Are the forward energy cascade associated with somewhat frontal\ninstabilities or interactions between balanced motions and internal waves? I hope the\nauthors can add more analysis to clarify the relevant mechanisms.\nThanks for requesting a clarification here. First, the convergent flows are predominately\nattributed to the ageostrophic secondary circulations at a front in the upper ocean, rather\nthan unbalanced internal waves. The ageostrophic secondary circulations that result from\nstrain-induced frontogenesis can be convergent (e.g., Hoskins and Bretherton 1972), as\ncan the circulations induced by mixed layer eddies (Capet et al., 2008) or boundary layer\nturbulence (McWilliams et al., 2015). Second, the mechanism of the forward energy\ncascade at submesoscale fronts is frontogenesis, as illustrated by Srinivasan et al. (2023).\nThe intention of this paper is to highlight that at the submesoscale the only dynamical\nquantity that matters for frontogenesis is horizontal convergence, and that the frontal\nforward energy flux is also proportional to the convergence.\nIn a parallel work (Savage et al., submitted to J. Phys. Oceanogr.), we have specifically\nexamined the role of near-inertial internal waves in the energy cascade. We carry out an\nenergy transfer analysis also using the coarse-graining approach to quantify the energy\nexchange rates between the internal wave field and mesoscale/submesoscale eddies.\nThe results show that the KE transfer between low-frequency flows (e.g.,\nmesoscale/submesoscale) and high-frequency waves (e.g., near-inertial waves) depends\non the characterization of low-frequency dynamics, i.e., the strength of the low-frequency\nKE and whether the low-frequency flow is dominated by strain or vorticity. These findings\nare largely consistent with Jing et al. (2018).\nIn response to the Reviewer’s comment, we now make explicit that unbalanced internal\nwave signals are removed from the measurements, and modify the manuscript to clarify\nthe mechanisms of convergent flows and forward energy cascade (lines 73-75, 122-124\nand 220-222).\nMinor comments\n1.Line 13: “remain unclear due to a lack of observations”. This statement is too strong\nbecause earlier theoretical and simulation studies have already pointed out the relevant\nmechanisms or routes.\nThank you for pointing this out. We now tone down this statement as “…are still\nunderstudied” (line 16).\n2.Line 22: Submesoscales are not always an oceanic energy sink it may also be an\nenergy source for mesoscales through inverse energy cascade.\nThe Reviewer is correct. We have modified this statement as “…the key role of\nsubmesoscale fronts in the oceanic kinetic energy cascade” (lines 25-26).\n3.Lines 44-48: The earlier theories of dynamic meteorology have already shown the role\nof convergent flows in the frontogenesis. You should also cite the much earlier references\nhere.\nThank you for this suggestion. Insights from earlier literature of dynamic meteorology,\nincluding Petterssen (1936), Sawyer (1956) and Hoskins (1982), has been incorporated\ninto the introduction of the revised manuscript (lines 53-54).\n4.Lines 59-63: Many recent studies based on high-resolution simulations have found that\nthe energy cascade in the submesoscale range is dominated by inverse energy cascade\n(e.g., Ajayi et al., 2021, JAMES; Zhang et al., 2023, NC). Is this because the resolution of\ntheir simulations is not enough to resolve the submesoscle frontogenesis ? The authors\nhighlight the importance of submesoscle frontogenesis in forward energy cascade here,\nbut the mesoscale strain-induced frontogenesis may also play a similar role.\nThis is a great comment. First, the model grid resolution employed in Ajayi et al. (2021)\nand Zhang et al. (2023) ranges from 1/48º to 1/60º, approximately equivalent to 1-3 km\ngrid spacing. These submesoscale-permitting simulations are expected to well resolve\nmixed-layer instabilities, but cannot adequately resolve submesoscale frontogenesis, as\npointed out by Naveira Garabato et al. (2022) and Srinivasan et al. (2023). Therefore, the\nmixed-layer instabilities, rather than submesoscale frontogenesis, are very likely the\ndominant mechanism determining the kinetic energy cascade in these simulations.\nSecond, we agree with the Reviewer that mesoscale strain-induced frontogenesis may\nplay a similar role. In fact, the submesoscale frontogenesis theory in Barkan et al. (2019)\nand our observational study here don’t necessarily exclude the occurrence of mesoscale\nstrain-induced frontogenesis. Our intent here is to highlight the point that only in the\nsubmesoscale frontogenesis scenario, forward energy transfer rate is proportional to the\nfrontal convergence.\nIn response to the Reviewer’s comment, we have now added the two relevant references\nmentioned by the Reviewer, and also included several sentences to clarify our findings\n(lines 73-75 and 78-83).\n5.Line 92 and Fig. 1h: Just based on result in one-day period, it is difficult to infer whether\nthe forward energy cascade is enhanced. I suggest extending the results in Figures 1c-h\nto one week to highlight the enhancement of forward energy cascade on the day shown\nhere.\nWe thank the Reviewer for pointing this out. Figure R7 below shows 1-week time series\nof kinetic energy transfer rates (added as Figure S2). We also add a sentence to make\nexplicit that the forward energy transfer rate during this event (10-7 m2 s-3) is one order of\nmagnitude larger than winter-mean energy transfer rate (lines 113-114), and extend the\nresults in Fig. 1c-h to 2 days in the manuscript (see revised Figure 1 in the manuscript).\n&'\nFigure R7: Time series of energy transfer rate Π% estimated at the central mooring from 1 to 9\nFebruary, 2013. The vertical dashed line denotes 14:07 UTC on 07 February 2013.\n6.Lines 112-113 and 240-241: The 16-hour low-pass filter (one inertial period) was used\nto obtain the sub-inertial motions. The obtained results actually also contain signals of\nsome remaining near-inertial waves (frequency of 0.8f-1.2f) and also diurnal tidal waves.\nIn order to totally remove the near-inertial waves and tidal signals, you’d better use 24-\nhour low-pass filter.\nWe have followed the Reviewer’s advice, and used a 24-hour low-pass filter in the revised\nmanuscript (lines 283-286). Note that 0.8f corresponds to 19.9 hours in the study region,\nand diurnal tidal waves are very weak in the study region (see Figure R3 above).\n7.Lines 127-129: You may cite more observational studies that support the skewness of\nsubmesoscale turbulence.\nWe thank the Reviewer for this useful suggestion. We have now added two recent\nobservational studies (Zhang et al., 2021JPO; Tarry et al., 2022 GRL) as references in\nline 153.\n8.Lines 158-160: In addition to the results during frontal events in Figures S4 and S6, I\nsuggest also showing the entire results using another supplementary figure (with frontal\nevents being marked using lines). By comparing the results during the periods with fronts\nand without fronts will help highlight the role of fronts.\nThis is a good point. We have followed the Reviewer’s advice and added figures to\ncompare the periods with and without fronts (see Figure S5 in the supporting information\nand Figure R8 below).\n&'\nFigure R8: Winter time series in the OSMOSIS mooring observations. (a) Π% (m2 s-3), the coarse-\ngrained horizontal energy flux from time scales longer than 2 days to shorter periods (with positive\nvalues indicating a downscale energy transfer), (b) −(cid:2) &' , the horizontal convergence smoothed\nat a 2-day scale, and (c) (cid:3)(cid:4) &' , the kinetic energy of scales shorter than 2 days. The mixed layer\ndepth as determined from glider measurements is shown by the black contour. Red and black\nblocks indicate frontal events defined by the region hosting |∇! (cid:5)| > 1 × 10() (cid:6) (& and\n−(cid:2) &' /(cid:1) >0.3, respectively.\n9.Lines 200-202: What is the mechanism causing the strong convergence? Is it due to\nthe remaining near-inertial waves? Please also refer to my 4th major comment and 6th\nminor comment.\nThanks for raising this issue again. First, we have now used a 24-hour low-pass filter to\nremove all variability in the internal wave band, and the results suggest that a forward\nenergy cascade can be found at submesoscale fronts. Second, Yu et al. (2022) show that\nnear-inertial waves are rather temporally intermittent (Figure R9 below), and do not\nalways match with strong convergence. Thus, the strong convergence is unlikely to be\ngenerated by near-inertial waves. In the revised manuscript, the text in lines 122-124 and\n220-222 has been altered to clarify this point. Please also see our reply to your major\ncomment 4.\nFigure R9: Time series of Wentzel-Kramers-Brillouin (WKB)-scaled near-inertial kinetic energy\nobserved by the current meters at the central mooring. The blue and pink lines, respectively,\nindicate the glider-based mixed layer depth HML and the H* scaling. The estimated downward\ngroup velocity of each event is indicated. Figure from Yu et al. (2022).\n10.Lines 203-205: Given that the fronts generated by convergent flows-induced\nsubmesoscale frontogenesis are usually very narrow (with very short length scale), their\nvertical scale or influence depth may also be small. So, their role in contacting the mixed\nlayer and deeper ocean may also be limited compared with the submesoscales with larger\nspatial scales.\nThe Reviewer is correct in that submesoscales with small horizontal scales are typically\nassociated with small vertical scale, and vice versa. We have toned down relevant\nstatements on the influence depth of rapid submesoscale frontogenesis (lines 239-241).\n11.Lines 212-216: Do the remaining near-inertial internal waves play a role in the forward\nenergy cascade? Please also refer to my 4th major comment and 6th minor comment.\nThanks again for raising this issue. Please see our response to your major comment 4\nand minor comment 9 above.\n12.Lines 261-263: There are also other meso- to submesocale resolving mooring arrays\nthat can certainly quantify the horizontal gradients of horizontal velocity and buoyancy\n(such as those deployed in the northwestern Pacific and South China Sea). I think you\nshould not ignore them here.\nOur apologies, this was a slip on our part. We now add these relevant studies (Zhang et\nal., 2021JPO; Zhang et al., 2022JGR; Zhang et al., 2024GRL) as references in line 307.\n13.Lines 285-293: Based on the density conservation equation, you can not obtain the\nvertical velocity within the mixed layer. How about using the continuity equation to\ncalculate the vertical velocity? If the calculated horizontal divergence is robust, you may\ndo so by assuming zero vertical velocity at sea surface.\nWe thank the Reviewer for directing us to this point. Unfortunately, we do not have\nmeasurements in the top 50-m depth range. To apply the continuity equation, we need\nto know the vertical distribution of the horizontal divergence, or assume depth\nindependent of the horizontal divergence in the top 50 m, which is very likely invalid\naccording to Tarry et al. (2022). We have clarified this point in lines 343-348.\nReferences\nAjayi, A., Le Sommer, J., Chassignet, E. P., Molines, J.-M., Xu, X., Albert, A., & Dewar,\nW. (2021). Diagnosing cross-scale kinetic energy exchanges from two submesoscale\npermitting ocean models. Journal of Advances in Modeling Earth Systems, 13 (6),\ne2019MS001923.\nBarkan, R., and McWilliams, J. C., 2017: Stimulated imbalance and the enhancement of\neddy kinetic energy dissipation by internal waves. Journal of Physical Oceanography,\n47, 181–198.\nCallies, J., Barkan, R., & Naveira Garabato, A. C. (2020). Time scales of submesoscale\nflow inferred from a mooring array. Journal of Physical Oceanography, 50(4), 1065-\n1086.\nCapet, X., McWilliams, J. C., Molemaker, M. J., & Shchepetkin, A. F. (2008). Mesoscale\nto submesoscale transition in the California Current System. Part III: Energy balance\nand flux. Journal of Physical Oceanography, 38(10), 2256-2269.\nHoskins, B. J., & Bretherton, F. P. (1972). Atmospheric frontogenesis models:\nMathematical formulation and solution. Journal of the Atmospheric Sciences, 29 (1),\n11-37.\nHoskins, B. J. (1982). The mathematical-theory of frontogenesis. Annual Review of Fluid\nMechanics, 14, 131–151.\nJing, Z., Chang, P., DiMarco, S. F., & Wu, L. (2018). Observed energy exchange between\nlow-frequency flows and internal waves in the Gulf of Mexico. Journal of Physical\nOceanography, 48(4), 995-1008.\nMcWilliams, J. C., Gula, J., Molemaker, M. J., Renault, L., & Shchepetkin, A. F. (2015).\nFilament frontogenesis by boundary layer turbulence. Journal of Physical\nOceanography, 45(8), 1988-2005.\nNaveira Garabato, A. C., Yu, X., Callies, J., Barkan, R., Polzin, K. L., Frajka-Williams, E.\nE., ... & Griffies, S. M. (2022). Kinetic energy transfers between mesoscale and\nsubmesoscale motions in the open ocean’s upper layers. Journal of Physical\nOceanography, 52(1), 75-97.\nPetterssen, S., 1936: Contribution to the theory of frontogenesis. Geofysiske\nPublikasjoner, 11(6), 1–27.\nSawyer, J.S., 1956. The vertical circulation at meteorological fronts and its relation to\nfrontogenesis. Proceedings of the Royal Society of London. Series A. Mathematical\nand Physical Sciences, 234(1198), 346-362.\nSrinivasan, K., Barkan, R., & McWilliams, J. C. (2023). A forward energy flux at\nsubmesoscales driven by frontogenesis. Journal of Physical Oceanography, 53(1),\n287-305.\nTarry, D. R., Ruiz, S., Johnston, T. S., Poulain, P.-M., Özgökmen, T., Centurioni, L. R., .\n. . others (2022). Drifter observations reveal intense vertical velocity in a surface ocean\nfront. Geophysical Research Letters, 49 (18), e2022GL098969.\nYu, X., Naveira Garabato, A. C., Vic, C., Gula, J., Savage, A. C., Wang, J., ... &\nMacKinnon, J. A. (2022). Observed equatorward propagation and chimney effect of\nnear-inertial waves in the midlatitude ocean. Geophysical Research Letters, 49(13),\ne2022GL098522.\nZhang, X., Zhang, Z., McWilliams, J. C., Sun, Z., Zhao, W., & Tian, J. (2022).\nSubmesoscale coherent vortices observed in the northeastern south china sea.\nJournal of Geophysical Research: Oceans, 127 (2), e2021JC018117.\nZhang, Z., Zhang, X., Qiu, B., Zhao, W., Zhou, C., Huang, X., & Tian, J. (2021).\nSubmesoscale currents in the subtropical upper ocean observed by long-term high-\nresolution mooring arrays. Journal of Physical Oceanography, 51 (1), 187–206.\nZhang, Z., Liu, Y., Qiu, B., Luo, Y., Cai, W., Yuan, Q., . . . others (2023). Submesoscale\ninverse energy cascade enhances Southern Ocean eddy heat transport. Nature\nCommunications, 14 (1), 1335.\nZhang, Z., Miao, M., Qiu, B., Tian, J., Jing, Z., Chen, G., ... & Zhao, W. (2024).\nSubmesoscale eddies detected by SWOT and moored observations in the\nnorthwestern Pacific. Geophysical Research Letters, 51(15), e2024GL110000.\nResponse to Reviewer 2\nThis paper presents compelling observational evidence of submesoscale frontogenesis\ndriven by horizontally-convergent strain flow. The data is consistent with previous\ntheoretical work from Barkan et al. 2019. This is an important finding because the\nconvergence-dominated frontogenesis events are likely unresolved in most ocean\nmodels. The strong, localized convergence also has significant implications for vertical\nsubduction and accumulation of buoyant material at fronts. I would recommend\npublication in Nature Communication after some minor revisions which are described\nbelow.\nWe thank the Reviewer for their supportive feedback, and hope the responses below help\naddress any remaining questions.\nThe introduction largely focuses on the theoretical aspects of frontogenesis and energy\ntransfers. Personally, I would have spent more time motivating the paper by discussing\nthe importance of the large vertical velocities and horizontal convergence that is observed\nat the submesocale fronts. In my view, this angle would provide a broader motivation.\nThanks for this useful comment. The Reviewer is correct in that the importance of large\nvertical velocities and horizontal convergence is indeed a strong motivation for this study.\nWe thus have shortened the theroretical aspects of frontogenesis (lines 40-46), and\nadded several sentences on the aspects of large vertical velocities and horizontal\nconvergence in the introduction so that our motivation appears broader (lines 66-71).\nDespite their centrality to the paper, submesoscale fronts and submesoscale\nfrontogenesis aren’t clearly defined in the paper. Submesocales are defined as having a\nscale less than 10km. This is ambiguous for a front where the along-front and cross-front\nlengthscales can be very different. I also don’t think that the scale is the most relevant\nmeasure. For example, it would be possible for a large-scale quasi-balanced flow to\nslowly deform a front so that the front remained well-approximated by QG or SG theory\nwell beyond the point where the cross front scale is less than 10km. I would suggest that\nthe authors should define a submesoscale front as one which is generated through\nfrontogenesis by submesoscale motions. In any event, these terms should be carefully\ndefined.\nWe have noted the Reviewer’s good point, and now make clear that the definition of the\nsubmesoscale range refers to the spatial scale of 200 m–20 km (lines 14 and 50), which\nis according to the latest review paper by Taylor and Thompson (2023) and is also\nconsistent with the majority of previous submesoscale studies. Submesoscale\nfrontogenesis is defined as the rate at which submesoscale buoyancy gradients intensify\n(lines 17-18), and submesoscale fronts are specifically referred to as those generated\nthrough submesoscale frontogenesis led by convergent flows (lines 66-67).\nThere have been several papers which have presented submesoscale and frontal\nstatistics from the OSMOSIS site where the measurements were collected. Although I\nrealize that space is limited in this journal, it would be helpful to briefly review this work\nand discuss how this papers fits amongst those findings.\nThis is a good suggestion. A brief summary and discussion of the OSMOSIS studies so\nfar, and how our paper fits in that context, are given in lines 212-222.\nminor comments:\nline 48: what does “tightly” refer to in this context?\nThanks for pointing this out. To avoid any confusion, we have removed “tightly” in the\nrevised manuscript (line 56).\nline 99: “eliciting” doesn’t seem like the right word.\n“To begin eliciting the mechanism” is now changed to “To begin with” (line 121).\nline 108: “This manifests” doesn’t sound right in this context\nThanks for spotting this. “This manifests” is now changed to “This indicates” (line 132).\nline 113: Why does this imply that the flow is not associated with internal waves?\nWe now add a sentence to make clear that we exclude high-frequency signals by applying\na 24-hour low-pass filter (lines 122-124). Thus, internal waves are expected to be\nremoved in the density and velocity data, and both thermal-wind terms exclusively reflect\ncontributions from sub-inertial flows.\nline 126: The wording needs to be improved here\nWe now re-phrase the sentence (lines 150-151).\nline 148: typo: “train”\nChanged to “strain”. Thank you!\nReferences\nTaylor, J. R., & Thompson, A. F. (2023). Submesoscale dynamics in the upper\nocean. Annual Review of Fluid Mechanics, 55, 103–127."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Comments on the revised manuscript by Yu et al. (2024)\nGeneral comments\nIn the revision, the authors have well addressed my previous concerns and their hard work is appreciated. Specifically, the\nauthors have demonstrated the robustness of the calculated KE transfer by adding a new subsection in the Methods, and\nalso clarified the characteristics and roles of internal waves in the study region. However, I still have several issues I think\nthe authors should address before the manuscript is accepted. The detailed comment are as follows.\nSpecific comments\n1.In order to remove the internal waves, the authors processed the moored data using a 24-hour low-pass filter before the\nformal analysis. However, this low-pass filter can also remove the super-inertial part of submesoscales, which tend to have\nstrong ageostrophic currents. How important is this super-inertial part of submesoscales in the submesoscale frontogenesis\nand the associated forward energy cascade? I think the authors should add some discussions about this point.\n2.Lines 191-193: One important conclusion of this paper is that submesoscale frontogenesis is strongly associated with the\nhorizontal convergence induced by ageostrophic secondary circulations (ASC). However, the authors fail to clarify the\npotential mechanisms accounting for the ASC. Although I understand that based on the present observations, it is difficult to\nprecisely determine the mechanisms, the authors should at least add more discussions about the likely mechanisms.\n3.Lines 90, 130-131, 183-184, 207-208: The authors found that the submesoscales and convergence can penetrate far\nbeneath the mixed layer base, which are consistent with other in situ observations. By combing this finding and my second\ncomment, I think the submesoscales or ASC are unlikely caused by the mixed-layer instability and boundary-layer\nturbulence, which are to a large degree confined within the mixed layer. The deep penetrating submesoscales or ASC may\nbe explained by the recently proposed mechanism called “mixed transitional layer instability” which discusses the\nsubmesoscale baroclinic instability by combing the surface mixed layer and subsurface transitional layer (Zhang et al., 2021\nJPO; Zhang 2024 OLAR).\n4.Line 63: In addition to “mixed-layer instabilities”, the above mentioned “mixed transitional layer instability” can also be\nresolved by the present submesoscale-permitting simulations, which may be responsible for the deep penetrating\nsubmesoscales.\n5.Line 211: In order to highlight your mechanism (i.e. convergence induced submesoscale frontogenesis) in future\nparameterization, you’d better briefly discuss the mechanisms of the present submesoscale parameterizations.\n6.Lines 224-225: In order to apply the parameterization of submesoscale frontogenesis to climate models, the models need\nto resolve the key mechanism accounting for the convergence. As mentioned by the authors, the present climate models\n(with resolutions lower than 0.1 degree) are too coarse to resolve the relevant processes of the ASC. So, such kind of new\nparameterization may be more suitable for the regional models that have much higher resolutions.", "reviewer_2": "The authors have made edits to the manuscript to address my previous comments. I just have two small comments on the\nrevised text.\nline 53: \"horizontal convergence\" isn't clearly defined. This sentence defines it as \"negative divergence\". I assume that this\nrefers to the horizontal divergence of the horizontal velocity field. However, the citations here consider frontogenesis driven\nby flows that are not horizontally divergent in this sense.\nline 66: A similar issue arises here. The phrasing \"driven by convergent flows\" is ambiguous. Does this refer to horizontally\nconvergent horizontal currents? What about frontogenesis driven by submesoscale eddies that aren't horizontally\nconvergent? If you want to keep the definition more broad, then I would suggest removing the phrase \"driven by convergent\nflows\". If something more specific is meant, then please clarify.\nline 356: I belive that what is being described here is Gaussian noise added to the velocity field which is then integrated to\nobtain the mooring location. This could be made more precise in the wording."}, "author_response": "Response to Reviewer 1\nGeneral comments\nIn the revision, the authors have well addressed my previous concerns and their hard\nwork is appreciated. Specifically, the authors have demonstrated the robustness of the\ncalculated KE transfer by adding a new subsection in the Methods, and also clarified the\ncharacteristics and roles of internal waves in the study region. However, I still have several\nissues I think the authors should address before the manuscript is accepted. The detailed\ncomment are as follows.\nWe thank the Reviewer for their constructive comments, which have helped in improving\nthe manuscript. Below, we describe how we have addressed these comments. Line\nnumbers refer to the revised version of the manuscript with tracked changes.\nSpecific comments\n1.In order to remove the internal waves, the authors processed the moored data using a\n24-hour low-pass filter before the formal analysis. However, this low-pass filter can also\nremove the super-inertial part of submesoscales, which tend to have strong ageostrophic\ncurrents. How important is this super-inertial part of submesoscales in the submesoscale\nfrontogenesis and the associated forward energy cascade? I think the authors should add\nsome discussions about this point.\nWe agree with the Reviewer that super-inertial submesoscale motions could be also\nimportant in inducing submesoscale frontogenesis and the associated forward energy\ncascade. We have included additional discussion on this point in lines 191-193.\n2.Lines 191-193: One important conclusion of this paper is that submesoscale\nfrontogenesis is strongly associated with the horizontal convergence induced by\nageostrophic secondary circulations (ASC). However, the authors fail to clarify the\npotential mechanisms accounting for the ASC. Although I understand that based on the\npresent observations, it is difficult to precisely determine the mechanisms, the authors\nshould at least add more discussions about the likely mechanisms.\nWe thank the Reviewer for highlighting this issue. We have now expanded the discussion\non the likely mechanisms for generating the ageostrophic secondary circulations.\nSpecifically, we clarify that mixed transitional layer instability may be an important\nunderlying mechanism, as the Reviewer points out. We also acknowledge that the\nstatistical diagnostics presented in this study may involve some combination of these\nmechanisms (lines 187-190).\n3.Lines 90, 130-131, 183-184, 207-208: The authors found that the submesoscales and\nconvergence can penetrate far beneath the mixed layer base, which are consistent with\nother in situ observations. By combing this finding and my second comment, I think the\nsubmesoscales or ASC are unlikely caused by the mixed-layer instability and boundary-\nlayer turbulence, which are to a large degree confined within the mixed layer. The deep\npenetrating submesoscales or ASC may be explained by the recently proposed\nmechanism called “mixed transitional layer instability” which discusses the\nsubmesoscale baroclinic instability by combing the surface mixed layer and subsurface\ntransitional layer (Zhang et al., 2021 JPO; Zhang 2024 OLAR).\nWe share the Reviewer’s opinion on the possible explanation for the deep penetrating\nsubmesoscales or ageostrophic secondary circulations. Indeed, the weak stratification of\nthe upper ocean in winter is conducive to the occurrence of mixed transitional layer\ninstability. We now make explicit that mixed transitional layer instability may be at play,\nand include these very relevant references (lines 187-189).\n4.Line 63: In addition to“mixed-layer instabilities”, the above mentioned“mixed\ntransitional layer instability” can also be resolved by the present submesoscale-\npermitting simulations, which may be responsible for the deep penetrating\nsubmesoscales.\nModified to include “mixed transitional layer instability” in the statement now (line 64).\n5.Line 211: In order to highlight your mechanism (i.e. convergence induced submesoscale\nfrontogenesis) in future parameterization, you’d better briefly discuss the mechanisms of\nthe present submesoscale parameterizations.\nThis is a good suggestion. We have included several sentences to briefly discuss the\npresent submesoscale parameterizations (lines 224-228).\n6.Lines 224-225: In order to apply the parameterization of submesoscale frontogenesis\nto climate models, the models need to resolve the key mechanism accounting for the\nconvergence. As mentioned by the authors, the present climate models (with resolutions\nlower than 0.1 degree) are too coarse to resolve the relevant processes of the ASC. So,\nsuch kind of new parameterization may be more suitable for the regional models that have\nmuch higher resolutions.\nThe Reviewer is correct. We have now clarified that the present climate models are too\ncoarse to accurately simulate the convergent ageostrophic secondary circulations, and a\nstep forward would be to parameterize such effects in regional models, which operate at\nmuch high resolutions (lines 235-239).\nResponse to Reviewer 2\nThe authors have made edits to the manuscript to address my previous comments. I just\nhave two small comments on the revised text.\nWe thank the Reviewer for their supportive feedback and hope the responses below help\naddress any remaining questions. Line numbers refer to the revised version of the\nmanuscript with tracked changes.\nline 53: \"horizontal convergence\" isn't clearly defined. This sentence defines it as\n\"negative divergence\". I assume that this refers to the horizontal divergence of the\nhorizontal velocity field. However, the citations here consider frontogenesis driven by\nflows that are not horizontally divergent in this sense.\nThank you for point this out. First, we now make clear that “horizontal convergence” refers\nto the convergence of the horizontal velocity field, and modify “negative divergence” to\n“negative horizontal divergence” (lines 42-43). We have also modified “convergence” to\n“horizontal convergence” throughout the manuscript to avoid any confusion.\nSecond, we include one new reference (Williams 1972), as well as Hoskins and\nBretherton (1972), Hoskins (1982). In the HB72 model it is shown that convergence is\nenhanced at a later stage of frontogenesis and is an important agent for driving super\nexponential growth. This is also explained in the review paper of Hoskins (1982).\nline 66: A similar issue arises here. The phrasing \"driven by convergent flows\" is\nambiguous. Does this refer to horizontally convergent horizontal currents? What about\nfrontogenesis driven by submesoscale eddies that aren't horizontally convergent? If you\nwant to keep the definition more broad, then I would suggest removing the phrase \"driven\nby convergent flows\". If something more specific is meant, then please clarify.\nWe have now removed the phrase “driven by convergent flows” as suggested (line 54).\nline 356: I belive that what is being described here is Gaussian noise added to the velocity\nfield which is then integrated to obtain the mooring location. This could be made more\nprecise in the wording.\nThank you for catching this. We have now revised the sentence and added a reference\nto clarify this point (lines 323-325).\nReferences\nWilliams, R. T., 1972: Quasi-geostrophic versus non-geostrophic frontogenesis. J. Atmos.\nSci., 29, 3–10."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have well adressed my comments. I recommend acceptance at the present stage.", "reviewer_2": "Response to Reviewer 2\nThis paper presents compelling observational evidence of submesoscale frontogenesis driven by horizontally-convergent strain flow. The data is consistent with previous theoretical work from Barkan et al. 2019. This is an important finding because the convergence-dominated frontogenesis events are likely unresolved in most ocean models. The strong, localized convergence also has significant implications for vertical subduction and accumulation of buoyant material at fronts. I would recommend publication in Nature Communication after some minor revisions which are described below.\n\nWe thank the Reviewer for their supportive feedback, and hope the responses below help address any remaining questions.\n\nThe introduction largely focuses on the theoretical aspects of frontogenesis and energy transfers. Personally, I would have spent more time motivating the paper by discussing the importance of the large vertical velocities and horizontal convergence that is observed at the submesocale fronts. In my view, this angle would provide a broader motivation.\n\nThanks for this useful comment. The Reviewer is correct in that the importance of large vertical velocities and horizontal convergence is indeed a strong motivation for this study. We thus have shortened the theroretical aspects of frontogenesis (lines 40-46), and added several sentences on the aspects of large vertical velocities and horizontal convergence in the introduction so that our motivation appears broader (lines 66-71).\n\nDespite their centrality to the paper, submesoscale fronts and submesoscale frontogenesis aren’t clearly defined in the paper. Submesocales are defined as having a scale less than 10km. This is ambiguous for a front where the along-front and cross-front lengthscales can be very different. I also don’t think that the scale is the most relevant measure. For example, it would be possible for a large-scale quasi-balanced flow to slowly deform a front so that the front remained well-approximated by QG or SG theory well beyond the point where the cross front scale is less than 10km. I would suggest that the authors should define a submesoscale front as one which is generated through frontogenesis by submesoscale motions. In any event, these terms should be carefully defined.\n\nWe have noted the Reviewer’s good point, and now make clear that the definition of the submesoscale range refers to the spatial scale of 200 m–20 km (lines 14 and 50), which is according to the latest review paper by Taylor and Thompson (2023) and is also consistent with the majority of previous submesoscale studies. Submesoscale frontogenesis is defined as the rate at which submesoscale buoyancy gradients intensify (lines 17-18), and submesoscale fronts are specifically referred to as those generated through submesoscale frontogenesis led by convergent flows (lines 66-67).\n\nThere have been several papers which have presented submesoscale and frontal statistics from the OSMOSIS site where the measurements were collected. Although I realize that space is limited in this journal, it would be helpful to briefly review this work and discuss how this papers fits amongst those findings.\n\nThis is a good suggestion. A brief summary and discussion of the OSMOSIS studies so far, and how our paper fits in that context, are given in lines 212-222.\n\nminor comments:\nline 48: what does “tightly” refer to in this context?\nThanks for pointing this out. To avoid any confusion, we have removed “tightly” in the revised manuscript (line 56).\nline 99: “eliciting” doesn’t seem like the right word.\n“To begin eliciting the mechanism” is now changed to “To begin with” (line 121).\nline 108: “This manifests” doesn’t sound right in this context\nThanks for spotting this. “This manifests” is now changed to “This indicates” (line 132).\nline 113: Why does this imply that the flow is not associated with internal waves?\nWe now add a sentence to make clear that we exclude high-frequency signals by applying a 24-hour low-pass filter (lines 122-124). Thus, internal waves are expected to be removed in the density and velocity data, and both thermal-wind terms exclusively reflect contributions from sub-inertial flows.\nline 126: The wording needs to be improved here\nWe now re-phrase the sentence (lines 150-151).\nline 148: typo: “train”\nChanged to “strain”. Thank you!\n\nReferences\nTaylor, J. R., & Thompson, A. F. (2023). Submesoscale dynamics in the upper ocean. Annual Review of Fluid Mechanics, 55, 103–127.\n\nResponse to Reviewer 2\nThe authors have made edits to the manuscript to address my previous comments. I just have two small comments on the revised text.\n\nWe thank the Reviewer for their supportive feedback and hope the responses below help address any remaining questions. Line numbers refer to the revised version of the manuscript with tracked changes.\n\nline 53: \"horizontal convergence\" isn't clearly defined. This sentence defines it as \"negative divergence\". I assume that this refers to the horizontal divergence of the horizontal velocity field. However, the citations here consider frontogenesis driven by flows that are not horizontally divergent in this sense.\nThank you for point this out. First, we now make clear that “horizontal convergence” refers to the convergence of the horizontal velocity field, and modify “negative divergence” to “negative horizontal divergence” (lines 42-43). We have also modified “convergence” to “horizontal convergence” throughout the manuscript to avoid any confusion.\nSecond, we include one new reference (Williams 1972), as well as Hoskins and Bretherton (1972), Hoskins (1982). In the HB72 model it is shown that convergence is enhanced at a later stage of frontogenesis and is an important agent for driving super exponential growth. This is also explained in the review paper of Hoskins (1982).\n\nline 66: A similar issue arises here. The phrasing \"driven by convergent flows\" is ambiguous. Does this refer to horizontally convergent horizontal currents? What about frontogenesis driven by submesoscale eddies that aren't horizontally convergent? If you want to keep the definition more broad, then I would suggest removing the phrase \"driven by convergent flows\". If something more specific is meant, then please clarify.\nWe have now removed the phrase “driven by convergent flows” as suggested (line 54).\n\nline 356: I belive that what is being described here is Gaussian noise added to the velocity field which is then integrated to obtain the mooring location. This could be made more precise in the wording.\nThank you for catching this. We have now revised the sentence and added a reference to clarify this point (lines 323-325).\n\nReferences\nWilliams, R. T., 1972: Quasi-geostrophic versus non-geostrophic frontogenesis. J. Atmos. Sci., 29, 3–10."}, "author_response": ""}]

Decision letter