# Impact of surface turbulent fluxes on the formation of roll vortices in a Mediterranean windstorm

Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau, Sophia E. Brumer

► To cite this version:

Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau, Sophia E. Brumer. Impact of surface turbulent fluxes on the formation of roll vortices in a Mediterranean windstorm. Journal of Geophysical Research: Atmospheres, 2024, 129 (22), pp.e2023JD040191. 10.1029/2023JD040191. hal-04252989v3

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<figure><img src="image_1.png" /></figure>
RESEARCH ARTICLE

10.1029/2023JD040191

**Key Points:**

* Large eddy simulations reveal the existence of roll vortices transporting strong winds to the surface in a Mediterranean windstorm

* Including the effects of sea spray in surface sensible heat fluxes reduces the size of rolls and increases momentum transport

* The results may constrain the representation of turbulent fluxes at the air-sea interface, which is uncertain under strong wind conditions

**Correspondence to:**

W. Lfarh,
[www.wiba.lfarh@meteo.fr](mailto:www.wiba.lfarh@meteo.fr)

**Citation:**

Lfarh, W., Pantillon, F., Chaboureau, J.-P., & Brumer, S. E. (2024). Impact of surface turbulent fluxes on the formation of roll vortices in a Mediterranean windstorm. *Journal of Geophysical Research: Atmospheres*, 129, e2023JD040191. https://doi.org/10.1029/2023JD040191

Received 25 OCT 2023
Accepted 24 OCT 2024

**Author Contributions:**

**Conceptualization:** Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau

**Formal analysis:** Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau, Sophia E. Brumer

**Funding acquisition:** Wahiba Lfarh

**Methodology:** Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau, Sophia E. Brumer

**Project administration:** Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau

**Resources:** Wahiba Lfarh, Florian Pantillon

**Supervision:** Florian Pantillon, Jean-Pierre Chaboureau

**Validation:** Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau

**Visualization:** Wahiba Lfarh, Florian Pantillon

**Writing – original draft:** Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau

© 2024. 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.

<figure><img src="image_2.png" /></figure>

# Impact of Surface Turbulent Fluxes on the Formation of Roll Vortices in a Mediterranean Windstorm

Wahiba Lfarh¹ ID, Florian Pantillon¹ ID, Jean-Pierre Chaboureau¹ ID, and Sophia E. Brumer¹ ID

¹LAERO, CNRS, UT3, IRD, Université de Toulouse, Toulouse, France

**Abstract** Roll vortices can have a significant influence on the exchanges of momentum, sensible heat and moisture throughout the boundary layer. They have been shown to reinforce air-sea interactions under strong wind conditions. This raises the question of how air-sea exchanges can, in turn, affect the roll vortices. However, representing surface turbulent fluxes during extreme wind conditions is a major challenge in numerical weather prediction and can lead to large uncertainties in surface wind speed. The sensitivity of rolls to different representations of surface fluxes is investigated using large eddy simulations. The study focuses on Mediterranean windstorm Adrian, where rolls are responsible for the transport of strong winds to the surface. Considering the effects of sea spray increases surface heat fluxes and significantly influences the roll morphology. The rolls become narrower and extend over a greater height, while the downward transport of momentum is intensified and results in higher wind speed near the surface. Roll vortices vanish within a few minutes in the absence of momentum fluxes, which maintain the wind shear necessary for their organization. They also quickly weaken without sensible heat fluxes, which sustain the near-neutral stratification required for their development. In contrast, latent heat fluxes play a minor role. These findings emphasize the necessity of precisely representing the processes occurring at the air-sea interface, which do not only affect the thermodynamic surface conditions but also the vertical transport of momentum within the windstorm.

**Plain Language Summary** Roll vortices are coherent and organized swirls that are often observed in the atmospheric boundary layer (the lowest part of the atmosphere). They are important because they can carry strong winds from higher in the atmosphere through the boundary layer toward the surface. For this study, roll vortices are simulated at high spatial resolution in a numerical model for a Mediterranean windstorm. The existence of roll vortices requires significant exchange of both heat and momentum between the sea and the atmosphere. The morphology of roll vortices is highly dependent on air-sea exchanges, which can be difficult to represent in numerical models under strong wind conditions. In particular, the evaporation of water droplets ejected by strong wind action on the waves may reinforce heat exchanges. When this effect is taken into account, the roll vortices are stronger, taller and narrower. Consequently, the wind speed increases near the surface. These findings highlight the need to better understand the interactions at the air-sea interface under windstorm conditions, because they act on the formation of damaging winds.

## 1. Introduction

Historically, meteorological research on mid-latitude cyclones has mainly focused on the synoptic scale and mesoscale (Bjerknes & Solberg, 1922; Carlson, 1980). At these scales, the cyclogenesis processes and the three-dimensional airflows are relatively well understood. Winds are often the root cause of damages brought by mid-latitude cyclones. However, submesoscale processes responsible for the transport of high momentum air to the surface remain poorly understood and predicted. Their scales represent a major challenge, because they are typically smaller than the grid size of numerical weather prediction systems (Sheridan, 2018).

In windstorms, besides deep convection (Ludwig et al., 2015) and convective showers (Browning et al., 2015), boundary-layer rolls can be responsible for transporting strong winds to the surface (Rivière et al., 2020). They are the main focus of this paper. Rolls are one of the most common forms of the atmospheric boundary layer (Young et al., 2002). They are defined as quasi-two-dimensional vortices, creating alternating upward and downward air motions (Etling & Brown, 1993; Lemone, 1973). Roll vortices are approximately oriented in the mean wind direction and their vertical extension is generally determined by the height of the boundary layer. These structures typically persist for 1–6 hr, with highly variable wavelength $\lambda$ (i.e., the distance between two ascending or descending branches) ranging from a few hundred meters to a few kilometers (Weckwerth et al., 1997). Rolls are
Writing – review & editing:

Wahiba Lfarh, Florian Pantillon, Jean-Pierre Chaboureau, Sophia E. Brumer

observed in different meteorological conditions such as cold-air outbreaks (Chen et al., 2019; Gryschka & Raasch, 2005) and hurricanes (Foster, 2005; Gao et al., 2017; Li et al., 2021). They are known for transporting momentum, heat, and moisture through their descending and ascending branches across the atmospheric boundary layer (Weckwerth et al., 1999).

The thermodynamic condition of the marine atmospheric boundary layer is strongly influenced by turbulent air-sea fluxes, which are particularly complex in windstorm situations. Heat fluxes, in particular, are among the diabatic processes involved in the development of mid-latitude cyclones. The resulting release of latent heat during condensation processes can strengthen vorticity at lower levels and therefore contribute to cyclogenesis (Booth et al., 2012; Ludwig et al., 2014). Air-sea interactions also play a significant role in modulating surface wind speeds during windstorms, as heat fluxes promote shallow convection and facilitate wind mixing from the upper boundary layer toward the surface (Schultz & Sienkiewicz, 2013).

The importance of air-sea interactions has led to widespread interest in improving their representation in numerical weather prediction systems (Lewis, Castillo Sanchez, Arnold, et al., 2019). Air-sea interactions occur at subgrid scales and necessitate semi-empirical parameterizations built on available data. To date, many uncertainties persist in air-sea flux estimates in windstorm conditions, as measurements are largely limited to wind speeds under 20 m s⁻¹. Although direct measurements from ocean buoys, GPS dropsondes, and airborne radar can be employed to quantify surface fluxes under strong wind conditions, the scarcity of such observations presents major challenges for model validation (Richter & Stern, 2014; Zou et al., 2018). In addition, the air-sea interface becomes more complex under strong wind conditions, with the presence of foam and sea spray resulting from breaking waves. These factors make measuring and modeling surface turbulent fluxes all the more difficult (Emanuel, 2003; Sroka & Emanuel, 2021).

In this context, theoretical studies and numerical simulations have shown that the microphysical processes governing the generation and evaporation of sea spray can have a significant impact on air-sea exchanges. As they float in the air, spray droplets carry a large amount of energy due to their speed and abundance, generating more intense momentum fluxes and modifying surface drag at the air-sea interface (Sroka & Emanuel, 2022; Veron et al., 2012). In addition, sea spray has the effect of cooling the air and transferring latent heat to the atmosphere when it evaporates, creating favorable conditions for more powerful heat exchange between the sea surface and the atmosphere (Andreas et al., 2015; Jeong et al., 2012). For instance, Zhao et al. (2017) found that sea spray caused an increase in tropical cyclone intensity by strengthening air-sea fluxes, while Sroka and Emanuel (2021) and Rizza et al. (2021) concluded that the inclusion of sea spray in surface turbulent flux parameterizations is crucial in extreme wind situations.

The Mediterranean area is an ideal test-bed for investigating the complex air-sea processes under strong wind conditions. It is one of the most active cyclogenetic regions in the Northern Hemisphere (Alpert et al., 1990; Trigo et al., 1999) and regional winds bring cold, dry continental air over the warm waters of the Mediterranean Sea, leading to intense air-sea interactions (Flamant, 2003). In this cyclogenesis-prone region, low-pressure systems are reinforced by exchanges resulting from contrasts in temperature and humidity between the atmosphere and the sea (Jansà et al., 1994). Ocean-atmosphere interactions and surface turbulent fluxes can also influence the mesoscale dynamics of Mediterranean windstorms (Richter & Stern, 2014; Varlas et al., 2017). Furthermore, surface fluxes can play an important role in creating near-neutral boundary layer conditions in a Mediterranean windstorm, allowing the high-momentum air to reach the surface (Brâncuș et al., 2019). The impact of surface fluxes on fine-scale transport processes, in particular on roll vortices, is largely unknown for Mediterranean windstorms. One reason is that these are often studied using numerical weather prediction models with a limited horizontal resolution of several kilometers at best, with few exceptions (Cioni et al., 2018).

How boundary layer rolls affect surface fluxes by transporting momentum, heat, and moisture has well been documented. In the case of hurricanes for instance, Morrison et al. (2005) and J. A. Zhang et al. (2008) found that surface fluxes are increased 2 to 3 times in the presence of rolls. The question of how fluxes in turn affect the rolls remains to be studied. The main objective of this work is to examine how turbulent fluxes at the air-sea interface influence the formation and organization of roll vortices and, hence, surface winds during windstorm Adrian that affected the northwestern Mediterranean on 29 October 2018 (Lfarh et al., 2023). To achieve this purpose, sensitivity tests to different parameterizations of surface turbulent fluxes are carried out using large eddy
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Wind speeds at 10 m height at 15:30 UTC, from reference simulations at 1,000 m (a) and 200 m (b) horizontal resolution. The black squares represent the D1 and D2 domains in (a). The wind direction at 10 m is represented by the green arrows. In (b), the white square indicates the zoomed-in area of 20 by 20 km shown in Figure 5.</figcaption></figure>

simulations (LESs)—that is, simulations with a grid fine enough to explicitly resolve eddies containing most of the energy and responsible for most of the turbulent transport (Pope, 2004).

The paper is structured as follows: Section 2 briefly presents the modeling strategy, the parameterizations used to calculate surface turbulent fluxes and the analysis tools. Section 3 examines the influence of surface turbulent fluxes at the mesoscale, particularly on changes in the trajectory and intensity of the windstorm. Section 4 investigates the effects of parameterizations on fine scale rolls and surface winds before discussing the contribution of each kind of turbulent flux. Finally, Section 5 summarizes the main results.

## 2. Methods

### 2.1. Numerical Configuration and Sensitivity Experiments

Two reference simulations, a mesoscale one and the other a LES, are carried out with the Meso-NH non-hydrostatic atmospheric model (Lac et al., 2018) to study the strong mesoscale winds in windstorm Adrian and the fine-scale processes responsible for their transport to the surface, respectively. Both simulations share the same vertical grid with 72 levels reaching 22 km and a finer grid spacing near the surface (10 m at the first level). They are initialized at 06:00 UTC on 29 October 2018 from the operational analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) and run for 15 hr.

The mesoscale simulation covers a domain centered on the northwestern Mediterranean (domain D1 in Figure 1a) with a horizontal grid spacing of 1,000 m allowing explicit representation of deep convection. The LES is nested in the mesoscale simulation using a one-way nested method, where lateral boundary layer conditions are provided by the outer model for the inner model at every time step (Stein et al., 2000). It has a horizontal grid spacing of 200 m over a large domain covering part of the Mediterranean Sea and the whole of Corsica (domain D2 in Figure 1b). Both simulations are based on the same parameterization schemes, except for three. The mesoscale simulation uses the fifth-order weighted essentially non-oscillatory advection scheme for momentum variables (Shu & Osher, 1988), the EDMF (eddy-diffusivity mass flux) parameterization of Pergaud et al. (2009) for shallow convection, and the 1D version of the scheme of Cuxart et al. (2000) for turbulence. In the LES, the EDMF parameterization is deactivated, as convection is explicitly represented, and a more accurate fourth-order centered advection scheme is used along with a 3D version of the turbulence scheme. As shown by Lfarh et al. (2023), the 200 m grid spacing is sufficient at explicitly resolving most of the turbulent kinetic energy and entering the inertial subrange for altitudes of $z \approx 200$ m and above, thus qualifies as LES. Closer to the surface, however, turbulence remains parameterized mainly, even at finer horizontal grid spacing down to 50 m. For further details on the simulation configuration, the reader is referred to Lfarh et al. (2023).
<table><caption>**Table 1**
Configuration of Control and Sensitivity Experiments</caption><thead><tr><th>Simulation</th><th>Grid mesh (m)</th><th>Domain</th><th>Period (UTC)</th><th>Air-sea fluxes</th></tr></thead><tbody><tr><td>Coare1</td><td>1,000</td><td>D1</td><td>06:00-21:00</td><td>COARE</td></tr><tr><td>Andreas1</td><td>1,000</td><td>D1</td><td>12:00-18:00</td><td>ANDREAS</td></tr><tr><td>Ecume1</td><td>1,000</td><td>D1</td><td>12:00-18:00</td><td>ECUME</td></tr><tr><td>Wasp1</td><td>1,000</td><td>D1</td><td>12:00-18:00</td><td>WASP</td></tr><tr><td>Coare2</td><td>200</td><td>D2</td><td>06:00-21:00</td><td>COARE</td></tr><tr><td>Andreas2</td><td>200</td><td>D2</td><td>15:00-15:30</td><td>ANDREAS</td></tr><tr><td>Ecume2</td><td>200</td><td>D2</td><td>15:00-15:30</td><td>ECUME</td></tr><tr><td>Wasp2</td><td>200</td><td>D2</td><td>15:00-15:30</td><td>WASP</td></tr><tr><td>NoM</td><td>200</td><td>D2</td><td>15:00-15:30</td><td>No momentum fluxes</td></tr><tr><td>NoH</td><td>200</td><td>D2</td><td>15:00-15:30</td><td>No sensible heat fluxes</td></tr><tr><td>NoLE</td><td>200</td><td>D2</td><td>15:00-15:30</td><td>No latent heat fluxes</td></tr></tbody></table>

Sensitivity experiments to turbulent fluxes at the air-sea interface are carried out at both scales based on the two reference simulations. In order to assess the impact of surface turbulent flux parameterizations on the evolution of windstorm Adrian at mesoscale, a first series of sensitivity experiments are performed with a horizontal grid spacing of 1,000 m on the D1 domain. These simulations are initialized at 12:00 UTC from the reference mesoscale simulation and run for 6 hr, including the development and intensification phases of windstorm Adrian. To shed light on the impact of turbulent exchanges between the air and the sea on the rolls that bring strong winds to the surface, a second series of sensitivity experiments is performed at a horizontal resolution of 200 m on the D2 domain. These experiments are initialized from the reference LES and conducted over a short period from 15:00 to 15:30 UTC, when the windstorm reaches its maximum intensity.

Surface-atmosphere interactions are managed by a surface modeling platform called SURFEX (Surface Externalized), which is coupled to Meso-NH (Masson et al., 2013). This platform integrates several physical models that deal with the different characteristics of the surface of the Earth. Surface turbulent fluxes are calculated as a function of atmospheric forcings from Meso-NH for the air temperature, specific humidity, horizontal wind components, pressure, total precipitation and radiative fluxes. The surface flux values are then transmitted to Meso-NH and injected into the turbulence scheme as boundary conditions. The Meso-NH model can further be coupled with an ocean model, but this capability appears of little relevance for the case of windstorm Adrian, because the sea surface temperature was relatively constant during the investigated period of 15 hr. In reference simulations, turbulent air-sea exchanges are represented by default using the COARE (Coupled Ocean-Atmosphere Response Experiment) 3.0 parameterization (Fairall et al., 2003). Three other parameterizations of air-sea exchanges widely used are tested at both 1,000 and 200 m resolutions and are described hereinafter. In addition to the different parameterizations, three other sensitivity experiments to momentum and heat fluxes are performed in this study. The aim is to isolate the impact of each type of flux on rolls and surface winds. Using the COARE reference parameterization, the NoM, NoH and NoLE simulations are performed at a horizontal resolution of 200 m, with momentum, sensible heat and latent heat fluxes set to zero, respectively. The simulations are labeled according to the name of the parameterization used, followed by “1” and “2” to refer to the horizontal resolutions of 1,000 and 200 m. The model configuration for each simulation is summarized in Table 1.

## 2.2. Parameterizations of Turbulent Fluxes at the Air-Sea Interface

Turbulent fluxes of momentum $\tau$, sensible heat $H$, and latent heat $LE$ are defined in terms of covariances as follows:

$$ 
\begin{aligned}
\tau &= \rho \overline{w' u'} \\
H &= \rho c_p \overline{w' \theta'} \\
LE &= \rho L_v \overline{w' q'}
\end{aligned} 
\qquad (1) 
$$
<figure><img src="image_4.png" /><figcaption>Figure 2. Surface turbulent fluxes of (a) momentum, (b) sensible, and (c) latent heat as a function of wind speed at 10 m from the Coare2 (green), Andreas2 (blue), Ecume2 (pink), and Wasp2 (orange) LESs at 15:30 UTC. Surface turbulent fluxes are calculated at each grid point in a region of strong wind speeds represented by the white square in Figure 1b.</figcaption></figure>

where $\rho$ is the air surface density, $c_p$ the heat capacity of air at constant pressure and $L_v$ the latent heat of vapourization. $u'$, $w'$, $\theta'$, and $q'$ correspond to turbulent fluctuations in horizontal and vertical velocity, potential temperature, and specific humidity, respectively. The overbars represent temporal averages.

Given that turbulent fluctuations cannot be represented explicitly in atmospheric models, turbulent fluxes are calculated using “bulk” parameterizations. Bulk algorithms are based on the determination of constants called exchange coefficients (or aerodynamic coefficients), which establish a relationship between turbulent fluxes and mean parameters. Turbulent fluxes are defined as a function of mean atmospheric variables at the surface as follows:

$$ 
\begin{align} 
\tau_{\text{bulk}} &= \rho C_D \Delta U^2 = \rho C_D (U_a - U_s)^2 \nonumber \\ 
H_{\text{bulk}} &= \rho c_p C_H \Delta U \Delta \theta = \rho c_p C_H (U_a - U_s)(\theta_a - \theta_s) \tag{2} \\ 
LE_{\text{bulk}} &= \rho L_v C_E \Delta U \Delta q = \rho L_v C_E (U_a - U_s)(q_a - q_s) \nonumber 
\end{align} 
$$

where $\Delta U$, $\Delta \theta$, and $\Delta q$ correspond to the difference in wind speed, potential temperature and specific humidity between the first atmospheric level (index a) and the sea surface (index s). $C_D$, $C_H$, and $C_E$ represent the exchange coefficients for momentum, sensible heat and latent heat, respectively.

Bulk parameterizations are for the most part based on the Monin and Obukhov (1957) similarity theory, which describes the mean vertical profiles of wind, temperature, and humidity in terms of empirically derived universal functions determining the departure of the roughness length dependent logarithmic profile given stability conditions. Bulk algorithms can differ in the choice of universal functions and parameterizations of the roughness length with various considerations of sea state impacts. However, none can be thoroughly validated in the high wind speed range (above 20 m s⁻¹) due to lack of measurements. Uncertainties are even larger when sea spray mediated fluxes are considered, because sea spray generation remains elusive. Thus, the present evaluation of the sensitivity to different air-sea parameterizations gives insight on the possible range of responses although the solution space may never be reached in reality.

In Meso-NH the surface fluxes are handled by the externalized surface model SURFEX, which is common to all the French atmosphere models from weather to climate, research to operational. In this article, four parameterizations used by the SURFEX community are considered: (a) COARE 3.0 mentioned above and used for reference simulations, (b) ECUME 6 (Belamari, 2005) the sixth version of Exchange Coefficient Unified Multi-campaign Experiments used operationally by Météo-France, (c) WASP (Bouin et al., 2024) the new Wave-Age Stress dependent Parameterization, and (d) ANDREAS (Andreas et al., 2015) which includes sea spray mediated heat fluxes. All four algorithms use the same stability functions. COARE and WASP differ in the Charnock parameterization used in the estimate of the dynamic roughness length. In ECUME 6 and ANDREAS transfer coefficients are roughness length independent. More details on each algorithm are given in Appendix A.
To highlight the differences between the parameterizations, the momentum, sensible and latent heat fluxes as a function of wind speed at 10 m are shown in Figure 2. For details on the wind speed dependence of the transfer coefficients, the readers are referred to Appendix A and the cited references for each parameterization. Fluxes are output from the LESs in the region of high winds in a narrow belt along the southern flank of the low-pressure center at 15:30 UTC, where they exceed 40 m s⁻¹ (white square in Figure 1b). All four parameterizations give comparable momentum fluxes below ≈30 m s⁻¹ and diverge above (Figure 2a). The strongest momentum fluxes are produced by COARE 3.0 followed by ANDREAS, which both continue to increase rapidly with wind speed. In contrast, the momentum fluxes given by ECUME and WASP for winds above 30 m s⁻¹ are much lower and tend to saturate.

These tendencies are contrasting by design, because the drag coefficients of ECUME and WASP are reduced at high winds to fit direct and indirect observations. Such observations are not taken into account in COARE and ANDREAS, whose validity range in that wind regime is debatable. While there is no consensus to date as to whether the drag coefficient in high winds is constant or decreases (e.g., Curcic & Haus, 2020), the different parameterizations used here are indicative of the upper (likely overestimated) and lower bounds of those commonly used.

The differences between sensible and latent heat flux parameterizations become apparent at speeds of 20 m s⁻¹ and above (Figures 2b and 2c). The COARE, ECUME, and WASP parameterizations show similar trends of heat fluxes at high speeds, varying between 200 and 500 W m⁻² for sensible heat fluxes, and between 500 and 1,500 W m⁻² for latent heat fluxes. ANDREAS reveals large deviations for wind speeds over 20 m s⁻¹ due to sea spray mediated fluxes. This translates into fluxes in excess of 2,000 W m⁻² and 4,000 W m⁻² for sensible and latent heat, respectively, at wind speeds over 45 m s⁻¹. It is worth noting that the fluxes given by the ANDREAS parameterization are likely overestimated and are prone to uncertainties due to the lack of observations to validate spray generation and the effect of droplets on air-sea momentum and heat fluxes. However, this paper focuses on the effect of increased turbulent heat flux rather than on the parameterization itself.

## 2.3. Auto-Correlation Function (ACF)

As in Lfarh et al. (2023) fine-scale wind speed structures associated with windstorm Adrian are characterized using the spatial auto-correlation function (ACF). The ACF is a statistical approach commonly used to assess the spatial variability of turbulence organization in the atmospheric boundary layer, defining the main shape, direction and characteristic size of structures (Brilouet et al., 2023; Salesky et al., 2017; Wilson & Wyngaard, 1996). In practice, the ACF measures the correlation of a variable with itself at spatial positions shifted along the x and y directions. In this case study, the 2D ACF $R_F(\delta_x, \delta_y)$ is calculated from the vertical wind speed fields $F(x, y)$ at lags $\delta_x$ and $\delta_y$, using the method of Granero Belinchon et al. (2022) as follows:

$$R_F(\delta_x, \delta_y) = \langle F(x, y) \times F(x + \delta_x, y + \delta_y) \rangle \quad (3)$$

where $F(x,y)$ is the field value at position $(x, y)$, $F(x + \delta_x, y + \delta_y)$ is the field value at a position lagged by $(\delta_x, \delta_y)$ from $(x,y)$ and $\langle \dots \rangle$ denotes the spatial average.

In the first step, the main shape of the structures is extracted. It can be either elliptical, suggesting the presence of rolls, or circular, as in the case of convective cells. The analysis is based on the integral length $L_{es}$, defined as the integral of the ACF where the field $F(x, y)$ remains correlated with itself. $L_{es}$ is calculated in different directions to detect possible anisotropy (Lohou et al., 2000). The geometry of the structures is determined by fitting the set of points corresponding to $L_{es}$. An elliptical fit indicates an elongated, elliptical structure, while a circular fit suggests a circular structure. In a second step, the geometric parameters of the structure are determined, including the major axis $r_a$ and the minor axis $r_b$. These two axes are used to quantify the flatness parameter $f$ calculated as follows:

$$f = \frac{r_a - r_b}{r_a} \quad (4)$$

This parameter is used to distinguish roll structures, where $f$ tends toward 1, from cellular structures, where the parameter tends toward 0. In a third step, the length scale of the organized structure $L_{os}$, which represents its
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a) Trajectories of Adrian as observed (best track, black line) and simulated by Coarel, Andreas1, Ecume1 and Wasp1 (colored lines) every 15 min between 12:00 and 17:00 UTC. The black circular markers indicate the observed position every hour. The terrain height is represented on domain D2. The best track is estimated from the center of the cyclonic cloud roll-up on the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) High Resolution Visible satellite image, while simulated trajectories are calculated from the position of the mean sea level pressure (MSLP) minimum. (b) Temporal evolution of the MSLP minimum and (c) of the 99th percentile of wind speed at 10 m over sea. The evolutions are calculated over the sea part of the D2 domain between 12:00 and 18:00 UTC.</figcaption></figure>

characteristic size, is estimated. This length is defined as the distance between two correlation maxima in the ACF.

# 3. Mesoscale Dynamics of Windstorm Adrian

## 3.1. Overview

In late October 2018, synoptic conditions in western Europe were marked by a mid-tropospheric trough formed over the eastern Atlantic, extending from Scandinavia to the Iberian Peninsula (Cavaleri et al., 2019; Davolio et al., 2020; Giovannini et al., 2021). On 29 October, the strongly baroclinic environment led to the formation of a large low-pressure region in the western Mediterranean, to the east of the trough axis. Due to a high contrast between the cold air and the warm sea surface, the low-pressure system evolved into a windstorm named Adrian (also known as Vaia). The windstorm rapidly intensified, reaching a minimum pressure of 977 hPa as it moved between Corsica and northwest Italy. In the morning, the passage of the cold front over Corsica and Sardinia triggered the formation of a thunderstorm system in Corsica, resulting from the combination of thermal instability and abundant humidity. Intense convection developed over Italy, resulting in heavy rainfall that reached 500 mm in 48 hr over northeastern Italy (Davolio et al., 2020). While only one person was injured in France, Adrian caused 12 deaths in Italy and a dramatic impact on the environment (Forzieri et al., 2020). In Corsica, Adrian produced wind gusts in excess of 180 km h⁻¹, causing extensive damage to infrastructure and considerable economic losses. The strong winds had their origin from a mesoscale cold conveyor belt, which refers to a cold air flow in the lower levels of the troposphere (Lfarh et al., 2023).

## 3.2. Impact of Surface Fluxes

The effects of the four parameterizations of surface fluxes are assessed here on the mesoscale evolution of windstorm Adrian. The observed and simulated trajectories from Coarel, Andreas1, Ecume1 and Wasp1 with a horizontal resolution of 1,000 m are shown over the D2 domain from 12:00 to 17:00 UTC, until the cyclone moves out of the domain and arrives on land (Figure 3a). At 12:00 UTC, Adrian is located to the west of Sardinia, then moves northwards along a meridional trajectory. It approaches Corsica between 15:00 and 16:00 UTC. All simulated trajectories remain close to the best track, demonstrating the ability of the model to capture the trajectory of Adrian. Furthermore, the simulated trajectories remain close to each other despite slight positional shifts. This suggests that the track of Adrian over this short period does not depend much on the air-sea flux parameterization used but is mainly determined by synoptic-scale dynamics.

Temporal evolutions of mean sea level pressure (MSLP) and 99th percentile wind speeds at 10 m over the sea are calculated from 12:00 to 18:00 on the D2 domain (Figures 3b and 3c). The evolution of MSLP indicates that Adrian intensifies rapidly, reaching its maximum intensity between 15:00 and 16:00 UTC, with 975 hPa in Coarel (Figure 3b). For this reason, sensitivity tests to the different parameterizations at a horizontal resolution of
<figure><img src="image_6.png" /><figcaption>**Figure 4.** (a) Maximum wind speed at 10 m observed between 12:00 and 18:00 UTC at stations in Corsica. Markers with large circles correspond to 11 coastal stations recording wind speeds exceeding 20 m s⁻¹. (b) Box plots of the bias and root-mean-square error (RMSE) between simulated and observed wind speeds at the 11 coastal stations, calculated over the period 12:00 to 18:00 UTC every 6 min. Boxes represent simulations Coarel, Andreas1, Ecumel, and Wasp1 in green, blue, pink and orange colors, respectively.</figcaption></figure>

200 m will be presented at 15:30 UTC. The MSLP then begins to rise gradually from 16:00 UTC onward, indicating the beginning of the weakening of Adrian. During the first 2 hr, all simulations show a similar evolution. The differences become perceptible from the moment of maximum intensity. The Ecumel and Wasp1 simulations show an evolution similar to that of Coarel, despite a slightly more pronounced deepening in Ecumel. Andreas1 shows a distinct evolution and a deeper cyclone. The pressure difference with the reference simulation does not exceed 0.5 hPa between 15:00 and 16:00 UTC, but reaches 1.5 hPa at 18:00 UTC.

In the early afternoon, wind speeds exceed 25 m s⁻¹ due to the intensification of the low-pressure system and increase rapidly to reach a peak at around 15:00 UTC, with 99th percentile values of 29 m s⁻¹ for Coarel (Figure 3c). As Adrian weakens, wind speeds gradually decrease until 18:00 UTC. Unlike the MSLP, wind speed evolutions show immediate differences at the start of the simulations, becoming more noticeable during the maximum intensity of the cyclone. The difference reaches 1 m s⁻¹ in Ecumel and Wasp1 compared with Coarel, and rises to 2 m s⁻¹ in Andreas1. The intensity differences obtained with the ANDREAS parameterization are consistent with the results of Perrie et al. (2005) and W. Zhang et al. (2006), who found that including sea spray in the surface fluxes leads to a decrease in surface pressure by a few hPa during windstorms and an increase in surface wind speed by a few m s⁻¹. Moreover, as in the case of Adrian, these authors found that sea spray has a minor effect on the windstorm trajectory. As the saturation of the drag coefficient is not taken into account in the COARE parameterization, it is not surprising that the Coarel simulation produces the lowest wind speeds compared with the other simulations. After 16:00 UTC, the differences become negligible and reflect an almost identical evolution of wind speeds.

Due to the passage of Adrian near Corsica, stations recorded high wind speeds, particularly in the western and northern coastal stations, where measurements exceeded 30 m s⁻¹ (Figure 4a). To evaluate how simulations with different parameterizations reproduce the observations, a comparative analysis of the different surface turbulent fluxes parameterizations is performed on 11 coastal stations (markers with large circles on Figure 4a). These 11 stations are selected on the basis of two criteria: proximity to the sea and wind speeds exceeding the critical threshold of 20 m s⁻¹, at which parameterizations begin to diverge from one another. Wind speed measurements at 10 m are recorded at 6-min intervals by the Météo-France surface weather network. To ensure a fair comparison, instantaneous wind speeds from the sensitivity tests are also averaged over 6-min periods, from 12:00 to 18:00 UTC. For the 11 stations, the simulations show a median bias of around -1.7 m s⁻¹, indicating a small underestimation of observed wind speeds. Minor differences are noted in root-mean-square error (RMSE). The median RMSE values are 4.09, 4.93, 4.37, and 4.06 m s⁻¹ for Coarel, Andreas1, Ecumel, and Wasp1, respectively (Figure 3b). These results suggest that simulations are somewhat more realistic with the COARE and WASP parameterizations compared to ECUME and slightly less with ANDREAS.
In conclusion, the four simulations reproduce station observations in a similar way, demonstrating that turbulent fluxes at the air-sea interface have little impact on wind speed over land. Over the short 6-hr period, the trajectory of the windstorm is unaffected by the choice of surface flux parameterization. This indicates that the trajectory is mainly determined by the large-scale flow. Regarding the intensity of Adrian, the inclusion of sea spray effects in the ANDREAS parameterization generates a more pronounced low-pressure system and slightly higher wind speeds compared to the reference parameterization COARE. Consequently, LES sensitivity tests can be carried out over short periods to assess the impact of turbulent exchanges at the air-sea interface on roll vortices, while preserving mesoscale characteristics of the windstorm.

# 4. Impact of Surface Turbulent Fluxes on the Fine Scale

## 4.1. Morphology of the Roll Vortices

In the following, the study focuses on a 20 km by 20 km region, representative of the narrow band of strong winds generated on the southern flank of the low-pressure center (white square in Figure 1b). Wind speeds lie above 20 m s⁻¹, a threshold at which turbulent flux parameterizations begin to diverge (Figure 2). The analysis is based on LESs, inspecting horizontal and vertical cross-sections of wind speeds (Figure 5). In the reference simulation Coare2, the horizontal section (Figure 5a) illustrates band-like wind structures where speeds exceed 48 m s⁻¹. The structures are approximately oriented in the wind direction from the southwest (red arrows). Horizontal sections are shown at z = 200 m, because the structures are well marked at this altitude. The vertical extent of the structures is roughly equivalent to the height of the boundary layer zᵢ, which reaches around 700 m (Figure 5b). The wind vectors show that regions of strong winds correspond to downdrafts and regions of weak winds to updrafts. Also, the wind structures are visualized as a regular alternation between upward and downward velocities, for example, at a horizontal distance between 10 and 12 km in Figure 5b. This reflects a helical circulation forming boundary layer rolls. Above the boundary layer, clouds form as bands aligned in the wind direction (cloud streets, not shown). These results are in line with the findings of Lfarh et al. (2023), who showed that the boundary layer is organized into rolls at 15:15 UTC in strong wind regions of windstorm Adrian. Such structures are found throughout the narrow belt of strong winds and persist until the weakening phase of the windstorm. Lfarh et al. (2023) used the same numerical setup as in Coare2 and found little sensitivity of the rolls to horizontal resolution between 50 and 200 m.

The boundary layer organization in Ecume2 and Wasp2 is similar to that in the reference simulation (Figures 5e-5h). The Andreas2 simulation stands out the most with coherent structures that are narrower than in Coare2 (Figure 5c). The upward and downward motions are more pronounced and extend over a greater vertical distance (Figure 5d). Accordingly, the boundary layer height is higher, showing marked fluctuations between 1,000 and 1,500 m.

The spatial characteristics of the rolls are examined in the four simulations using the ACF calculated from the vertical wind speed field at 15:30 UTC over the zoomed area shown in Figure 5. Figure 6a first presents vertical profiles of the flatness parameter *f*. Following Brilouet et al. (2023), a threshold is chosen to distinguish roll structures with *f* > 0.7 from disorganized structures with *f* < 0.7. In Coare2, the flatness parameter reveals the presence of rolls up to *z* = 400 m and a transition into disorganized structures above. The mean wind direction varies slightly with height, from 60° to 50° clockwise, while the roll direction evolves counter-clockwise from 50° to 70° (Figure 6b). Below *z* = 400 m, this results in rolls mainly oriented in the wind direction, with a minor difference of around 10°. This agrees with observational studies that have shown that rolls are oriented between 10° and 20° from the mean wind direction (Atkinson & Wu Zhang, 1996; Foster, 2005), unlike streaks that are another type of organized boundary layer structures often oriented between 15° and 30° from the mean wind direction (Young et al., 2002). Finally, the size of rolls reaches 2,000 m, giving an aspect ratio *λ/zᵢ* of 2.73. Altogether, the results imply that elliptical roll structures are present below 400 m in Coare2. The morphological characteristics of the rolls at 15:30 UTC are comparable to those found at 15:15 UTC in Lfarh et al. (2023), except for the size of the rolls that was slightly larger, reaching 2,400 m, with little sensitivity to the horizontal resolution.

In the Ecume2 and Wasp2 simulations, the size of the rolls varies slightly between 2,200 and 2,400 m but remains comparable to that in the reference simulation. The other morphological characteristics are similar (Figures 6a and 6b). For Andreas2, however, the flatness parameter remains more constant with height, the direction of the rolls stays closer to the mean wind direction and their size is smaller and reaches 1,400 m only. The aspect ratio in
<figure><img src="image_7.png" /><figcaption>**Figure 5.** (left) Horizontal sections at *z* = 200 m and (right) vertical sections of horizontal wind speed at 15:30 UTC from (a, b) Coare2, (c, d) Andreas2, (e, f) Ecume2, and (g, h) Wasp2. The black lines in the horizontal sections show the location of the vertical sections perpendicular to the mean wind, while the red vectors show the horizontal wind. The thick red line in the vertical sections corresponds to the height of the boundary layer, while the vectors show the wind in the sections.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Vertical profiles of (a) flatness parameter *f* and (b) direction of the mean wind (dotted curves) and of the structures (solid curves), identified from the auto-correlation function over the zoomed domain in Figure 5 at 15:30 UTC. Dashed lines in (a) indicate the average boundary layer height for each simulation.</figcaption></figure>

Andrea2 is 1.27, which indicates that the rolls are narrower in comparison to the height of the boundary layer. Table 2 summarizes the descriptive parameters of the rolls in the different simulations. Altogether, the number of rolls over the narrow band of strong winds (distance of about 20 km) is *n* ≈ 10 in Coare2, *n* ≈ 8 in Ecume2 and Wasp2, and *n* ≈ 14 in Andreas2.

## 4.2. Vertical Wind Transport by the Rolls

Over the same region shown in Figure 5, the wind speed increases progressively from *z* = 1,200 m downward and reaches a maximum near *z* = 400 m, then decreases when approaching the surface (Figure 7a). The maximum wind speed in the middle of the boundary layer corresponds to the cold conveyor belt causing the strong mesoscale winds (Lfarh et al., 2023). In the Coare2 reference simulation, the virtual potential temperature profile shows a decrease from the surface up to an altitude of 200 m, indicating instability characterized by a warm, moist

surface layer (Figure 7b). Ecume2 and Wasp2 show a similar profile, with slightly higher temperatures in Ecume2. The surface temperature is higher and the vertical gradient is more pronounced in Andreas2, showing a rapid decrease with altitude. This is due to the enhanced surface fluxes of sensible and latent heat, which increase air temperature and humidity.

The boundary layer stability can be assessed with the stability parameter *ζ* = −*z*ᵢ/*L*, where *L* is the length of Monin and Obukhov (1957) and −*L* represents the distance above the surface where the production of buoyancy turbulence exceeds that of shear turbulence. In a fully convective boundary layer, that is, *ζ* ≫ 1, buoyancy dominates turbulence generation throughout the boundary layer (Khanna & Brasseur, 1998; Salesky et al., 2017). The values of *ζ* < 1 in Coare2, Ecume2 and Wasp2 (Table 2) indicate a quasi-neutral atmospheric boundary layer, where turbulence is produced by wind

<table><caption>**Table 2**

Descriptive Parameters of the Boundary Layer and of Roll Vortices in the Large Eddy Simulations Sensitivity Tests</caption><thead><tr><th>Simulation</th><th><i>L</i> (m)</th><th><i>z</i><sub>i</sub> (m)</th><th>ζ = −<i>z</i><sub>i</sub>/<i>L</i></th><th>λ</th><th>λ/<i>z</i><sub>i</sub></th></tr></thead><tbody><tr><td>Coare2</td><td>−1,453</td><td>732</td><td>0.50</td><td>2,000</td><td>2.73</td></tr><tr><td>Andreas2</td><td>−701</td><td>1,098</td><td>1.56</td><td>1,400</td><td>1.27</td></tr><tr><td>Ecume2</td><td>−1,089</td><td>780</td><td>0.71</td><td>2,400</td><td>3.07</td></tr><tr><td>Wasp2</td><td>−1,331</td><td>703</td><td>0.52</td><td>2,400</td><td>3.41</td></tr><tr><td>NoLE</td><td>−1,372</td><td>692</td><td>0.50</td><td>1,600</td><td>2.31</td></tr><tr><td>NoH</td><td>−∞</td><td>509</td><td>0</td><td>—</td><td>—</td></tr><tr><td>NoM</td><td>0</td><td>854</td><td>−∞</td><td>—</td><td>—</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Vertical profiles of (a) horizontal wind speed, (b) virtual potential temperature and (c) vertical fluxes of zonal momentum, calculated in the wind direction. The dotted horizontal lines in (a) indicate the boundary-layer height. The dashed, dotted and solid lines in (c) show the resolved, subgrid and total contributions, respectively. All profiles are averaged at 15:30 UTC over the area shown in Figure 5.</figcaption></figure>

shear mainly (dynamic production). The thermal instability increases by a factor of 2–3 in Andreas2 but the shear instability remains dominant.

The stability parameter is also widely used to predict roll organization. The ζ values obtained in the various simulations are consistent with the results of Khanna and Brasseur (1998), who found a boundary layer organized into rolls with a stability parameter ζ = 0.44. The results are also in line with the recent study of Stopa et al. (2022), which reveals that coherent roll structures occur in a slightly unstable but nearly neutral atmosphere. However, observational studies have shown that organized roll structures can appear for values of ζ up to 250 (Brümmer, 1999). This contrast was explained by Gryschka et al. (2008, 2014), who further distinguished two types of rolls depending on the value of the stability parameter. On the one hand, free rolls appear for small ζ values and pre-exist in a neutral or weakly stratified boundary layer, where they develop through pure self-organization of the flow. On the other hand, forced rolls appear for ζ values higher than 10 and are due to surface inhomogeneities (Kawase et al., 2005; Tripoli, 2005). The rolls found in windstorm Adrian with low ζ values over the open sea are therefore free rolls.

While roll vortices pilot vertical motion in the boundary layer, turbulence consisting of irregular eddies is one of the most important transport processes near the surface. This raises the question of the respective roles of rolls and turbulent motion in vertical momentum transport. The distinction is estimated here by the separation between resolved motion, which has been shown to consist in organized roll structures, and subgrid-scale motion represented by the turbulence scheme. This assumption likely overestimates the turbulent contribution, because fine-scale rolls are not fully resolved with 200 m horizontal grid spacing (Lfarh et al., 2023).

In Coare2, the sum of resolved momentum fluxes and subgrid-scale momentum fluxes, which corresponds to the total momentum transport, shows a gradual strengthening with decreasing height (solid green line in Figure 7c). Resolved momentum fluxes dominate at altitudes above *z* ≈ 200 m (dashed line), while they progressively decrease toward the surface and subgrid-scale motion becomes responsible for most of the momentum transport (dotted line). Vertical profiles in Ecume2 and Wasp2 remain similar to those observed in Coare2. In contrast, vertical profiles in Andreas2 reveal a clear distinction from the other simulations. The total transport is much greater both near the surface and aloft due to stronger resolved momentum fluxes, which dominate down to *z* ≈ 100 m. At *z* = 200 m, resolved fluxes are enhanced by 40% compared to the reference simulation. This enhanced downward transport in Andreas2 is consistent with the larger vertical extent of the rolls and explains the weaker winds in the middle of the boundary layer and the stronger winds near the surface compared to the other simulations (Figure 7a).
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Probability density functions (PDFs) of (a) vertical wind speed at 400 m height and horizontal wind speed at heights (b) 400 m and (c) 10 m. The vertical lines indicate the mean values in (b, c). The PDFs are calculated over the area shown in Figure 5.</figcaption></figure>

Interestingly, the enhancement in resolved vertical momentum transport by 40% in Andreas2 compared to Coare2 roughly matches the increase from $n \approx 10$ to $n \approx 14$ in the number of rolls over the narrow band of strong winds (or the decrease in their size from $\lambda = 2,000$ m to $\lambda = 1,400$ m). Thus, the transport of momentum per roll is equivalent between the two simulations and the smaller but more numerous rolls in Andreas2 imply a stronger total transport. In contrast, simulations Ecume2 and Wasp2 show values of resolved vertical momentum transport similar to Coare2 but with less, larger rolls ($n \approx 8$ and $\lambda = 2,400$ m), which also increases the transport of momentum per roll. The contrast can be explained by the weaker surface momentum fluxes in ECUME and WASP compared to the COARE and ANDREAS parameterizations (Figure 2a).

To assess the impact of the different parameterizations on horizontal and vertical winds in the middle of the boundary layer and near the surface, Figure 8 shows probability density functions at 400 m, where rolls begin to form, and at 10 m. As in the reference simulation, Ecume2 and Wasp2 show narrow distributions of vertical wind speeds at $z = 400$ m (Figure 8a). The standard deviation values of $0.9 \text{ m s}^{-1}$ in Coare2 and $0.7 \text{ m s}^{-1}$ in Ecume2 and Wasp2 indicate moderate vertical motion. Andreas2 shows a broader distribution and a standard deviation of $1.5 \text{ m s}^{-1}$ with a peak shifted toward negative velocities. This shows higher variability in vertical velocities, marked by more pronounced upward and downward motions. At $z = 400$ m, the horizontal wind speed is lower in Andreas2 compared to the other parameterizations, with a mean value of 46 instead of 47 $\text{m s}^{-1}$ (Figure 8b). The slower wind is explained by the enhanced downward transport of momentum at this altitude. Near the surface, the distribution of wind speeds differs more between the simulations. For Coare2, wind speeds are relatively low compared to Ecume2 and Wasp2 and this is consistent with the stronger surface fluxes of momentum with the COARE parameterization. In contrast, they are higher in Andreas2 than in all other simulations. This is explained by the more intense transport in Andreas2 (Figure 8c), which thus largely compensates for the strong surface momentum fluxes with the ANDREAS parameterization (Figure 2).

In summary, the increase in heat fluxes due to sea spray leads to a more important thermal instability at the air-sea interface. This instability generates more intense vertical circulations in the boundary layer, leading to the formation of narrower and more numerous rolls that extend higher than in the reference simulation. As a result, the momentum transport to the surface increases significantly, leading to stronger surface wind speeds.

### 4.3. Individual Contribution of Surface Fluxes

The findings presented in the previous section suggest that surface heat fluxes contribute significantly to the organization of roll vortices and surface winds in combination with surface momentum fluxes. This section focuses on the NoH, NoLE and NoM simulations to determine the role of each kind of surface turbulent flux separately from the others. Without latent heat flux (NoLE), the boundary layer organization into rolls (Figures 9c and 9d) is similar to that of Coare2 (Figures 9a and 9b). In the absence of sensible heat flux (NoH), strong wind speeds in the form of a large packet are confined between $z = 250$ m and a lower boundary layer height of around
<figure><img src="image_11.png" /><figcaption>**Figure 9.** As in Figure 5, for (a, b) Coare2 (c, d) NoLE, (e, f) NoH, and (g, h) NoM. For clarity, the color bar of wind speeds is scaled differently in NoM.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Temporal evolution of (a) flatness parameter, (b) direction, and (c) structure size of rolls vortices at *z* = 200 m, for Coare2 (green), NoH (red), NoLE (blue), and NoM (gold).</figcaption></figure>

*z* = 500 m (Figures 9e and 9f). The boundary layer is devoid of alternating upward and downward motions, which is due to the reduced heating of the surface layer. Without momentum flux (NoM), the wind speed is strongly enhanced (higher than 55 m s⁻¹ locally) and disorganized, reaching lower levels because friction forces are not taken into account (Figures 9g and 9h).

The evolution of the morphological parameters of rolls in Coare2, NoH, NoLE, and NoM is evaluated every minute for the full 30-min duration of the simulations to assess their persistence in response to surface fluxes. The elliptical shape of the coherent structures is retained over time in Coare2 with a flatness parameter *f* superior to 0.7 (Figure 10a). The difference between wind and structure directions does not exceed 20° (Figure 10b). Overall, characteristic roll sizes fluctuate between 2,000 and 3,000 m, with an average of around 2,100 m over 30 min (Figure 10c). Note that roll sizes are calculated with an accuracy of 200 m, that is, the resolution of the simulations. The NoLE simulation shows a similar evolution for all parameters, albeit with a modest deviation from Coare2, particularly at 15:30 UTC. Rolls in NoLE are on average slightly larger than in Coare2 with a size of around 2,300 m. Divergences from the reference simulation are immediately apparent in NoM, whereas they appear after about 5 min in NoH. In both simulations, the flatness parameter tends toward very low values, and the structures become misaligned with the wind direction. Given that characteristic sizes are defined for structures with a flatness parameter greater than 0.7, the ACF indicates that there is no spatial periodicity in the vertical velocity field. Consequently no roll structures are present after a few minutes of simulation in NoM and NoH.

Vertical wind speed profiles in the NoH and NoLE simulations are comparable to the reference simulation Coare2, with a slightly sharper decrease toward the surface in NoH (Figure 11a). In contrast, the NoM profile remains clearly distinct and high wind speeds remain almost uniform in the lower boundary layer. Unlike NoLE, which shows a decrease with height in virtual potential temperature in the surface layer similar to Coare2, NoH is distinguished by a profile that maintains an almost constant virtual potential temperature (Figure 11b). The stability parameter ζ tends to zero in that case, while ζ is no longer relevant in NoM (Table 2). A value of ζ = 0.50 in NoLE, as in Coare2, suggests that latent heat fluxes have weak impact on the atmospheric stability and on the

<figure><img src="image_13.png" /><figcaption>**Figure 11.** As in Figure 7, for Coare2, NoH, NoLE, and NoM.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Summary of the main results of the paper. Red and blue vertical arrows represent surface sensible and latent heat fluxes, respectively, while green horizontal arrows represent the background wind shear and circling arrows represents rolls. See text for details.</figcaption></figure>

formation of roll vortices. Although stability conditions are comparable, the momentum transport is somewhat weaker in NoLE (Figure 11c). This is attributed to the slightly higher roll size in NoLE, which results in fewer rolls in the region. In NoH, resolved fluxes are limited compared to the Coare2 simulation and result in lower total transport, particularly at altitudes below 400 m where roll structures are more pronounced in the reference simulation. Moreover, turbulent transport becomes dominant at higher altitude than in Coare2. Finally, the vertical transport profile in NoM is completely different from the other simulations and vanishes near the surface due to the absence of momentum fluxes.

In short, the absence of sensible heat flux inhibits the formation of roll structures even in the presence of intense shear. Consequently, momentum transport is reduced and is mainly controlled by turbulent fluxes. Likewise, without momentum fluxes, wind shear is impacted and rapidly slows down the formation of rolls. In contrast, the roll characteristics are weakly affected by the absence of latent heat fluxes.

**5. Conclusions**

Ensuring an accurate representation of air-sea fluxes is crucial for a better understanding of the marine atmospheric boundary layer dynamics. However, uncertainties persist in the parameterization of fluxes during windstorms due to the lack of observations for wind speeds above 20 m s⁻¹. Such strong winds occurred during the passage of the Mediterranean cyclone Adrian studied here. The main objective of this study is to investigate the role of air-sea fluxes in the formation of fine-scale rolls using LES with the Meso-NH atmospheric model. Roll vortices, rarely studied in mid-latitude windstorms, have been shown to be involved in the downward transport of strong winds associated with Adrian (Lfarh et al., 2023).

First, the impact of four air-sea flux parameterizations is examined using mesoscale simulations over a period of 6-hr. The parameterizations used differ in the formulation of surface fluxes of latent heat, sensible heat and momentum, and also in the way they take into account the effects of physical processes such as sea spray. The choice of surface flux parameterization does not affect the windstorm trajectory. This shows that, in the relatively short time period covering the mature phase of the cyclone, the trajectory is mostly driven by the large-scale flow, which joins results found in the study of a Mediterranean tropical-like cyclone (Ricchi et al., 2017). In addition, the intensity of windstorm Adrian shows a slight sensitivity to the inclusion of sea spray effects, which reinforces heat fluxes. As a result, the surface pressure drops by a few hPa more than in the other simulations and the surface wind speed slightly increases.

Second, the impact of the four parameterizations on the development and the organization of the rolls is examined through LES performed at a horizontal grid spacing of 200 m over a period of 30 min. Roll vortices are systematically formed in the strong wind region, whatever the air-sea flux parameterization used. A schematic summarizes the main results relative to the sensitivity of rolls to surface fluxes for this specific windstorm case
(Figure 12). When heat fluxes are moderate, rolls are characterized by sizes of around 2,000 m and extend vertically to the middle of the boundary layer (Figure 12, left panel). These values are typical of roll vortices, whose wavelength generally varies from 2 to 20 km with a vertical extent of 1–2 km, and which depend on thermal instabilities and wind shear (Etling & Brown, 1993).

However, the morphological characteristics of the rolls are significantly influenced by surface fluxes, in particular by increased heat fluxes resulting from sea spray. Stronger heat fluxes lead to more important thermal instability at the air-sea interface. Hence, vertical motions become more pronounced in the boundary layer. The roll structures formed in such conditions are of reduced size, greater in number, and exhibit a higher vertical extent (Figure 12, middle panel). Similarly, earlier studies showed that pronounced thermal instability in the boundary layer produces rolls with smaller wavelengths and consequently lower aspect ratios (Etling & Brown, 1993). Likewise, Glendenning and Burk (1992), found that a decrease in surface heat fluxes results in larger, less intense roll vortices losing their linear structure. Stronger heat fluxes significantly increase vertical momentum transport, which is attributed to structures organized as rolls before turbulence takes over close to the surface. This results in higher surface wind speeds, although surface momentum fluxes are also strengthened by sea spray. The increase in vertical momentum transport approximately matches the increase in roll number, which leaves the transport per roll unaltered. Hence, it is assumed that the transport in the presence of sea spray is enhanced by the larger number of rolls. Furthermore, the lower atmospheric stability results in a deeper boundary layer. This allows the rolls to form over a wider vertical extent and, consequently, to transport additional momentum from higher altitudes.

Third, the respective role of surface latent heat, sensible heat and moment fluxes is disentangled by performing LES sensitivity tests. Even in the absence of latent heat flux, rolls continue to form and retain similar characteristics, although their size is slightly affected. This indicates that latent heat fluxes have little impact on roll organization. In contrast, roll structures quickly disappear without sensible heat fluxes (Figure 12, right panel). They also disorganized within a few minutes without surface momentum fluxes. Both of these fluxes are directly responsible for the near-neutral conditions required to form and maintain rolls.

Since rolls are well known for their role in transporting momentum, the question arises as to the respective roles of rolls and turbulent motion in vertical momentum transport. In this paper, a distinction is made between resolved motion, associated with structures organized as rolls, and motion at the subgrid scale, represented by the turbulence scheme. It is found that the increase in resolved momentum fluxes also leads to an increase in total fluxes. In contrast, in a case of a cold-air outbreak Gryschka et al. (2014) showed that forced rolls contribute up to 50% but do not influence the total vertical transport, because they take over the part of unorganized turbulence. The contrast may be due to the distinguishing assumption between rolls and turbulent motion, which is sensitive to the horizontal resolution of the model and becomes inappropriate close to the surface. An interesting approach to better isolate the motion associated with roll structures and quantify contributions to momentum transport would be the conditional sampling method (Brient et al., 2019; Brilouet et al., 2020).

The interaction of surface fluxes with roll vortices is explored here under extreme conditions and contributes to the understanding of the processes involved in windstorms. The choice of specific surface flux parameterizations is driven by standards of the surface model SURFEX used in Meso-NH and other weather and climate models of the French community. The four used parameterizations are not necessarily the latest versions and may well exaggerate the effect of some physical processes but indicate upper and lower bounds of the range of formulations commonly used. In future work it would be interesting to test other parameterizations used by other scientific communities. The contribution of additional surface processes other than sea spray should also be considered. For instance, although foam is regularly observed at the air-sea interface in strong winds, experiments to measure its impact on surface fluxes are relatively recent (Sroka & Emanuel, 2021). The role of foam in roll formation and surface winds should be assessed and is probably a contribution to consider in improving surface flux parameterizations.

As shown in previous studies (Lfarh et al., 2023; Li et al., 2021), a LES approach is indispensable for understanding the fine-scale processes responsible for transporting strong winds downward, such as roll vortices in this study. The findings here highlight that, despite explicit representation of such processes, an incomplete description of the physical mechanisms at the air-sea interface under strong wind conditions can lead to significant discrepancies, which can have an impact on wind forecast. Furthermore, even with the fine horizontal grid spacing of 200 m (and down to 50 m in Lfarh et al. (2023)), a parameterization is still needed to represent turbulent motion near the surface. On the one hand, higher resolution would be required to explicitly represent the smallest
eddies but this would imply tremendous numerical costs due to the large spatial extent of the windstorm. On the other hand, such high resolution does not meet the stationarity hypothesis of the Monin and Obukhov (1957) similarity theory the surface flux parameterizations are based on. Thus, a new framework may be needed to represent surface turbulent fluxes in an appropriate way.

Apart from the turbulent fluxes, the wave-induced roughness modifies the boundary-layer momentum, heat and humidity at the air-sea interface. Research has shown that the atmosphere-wave coupling, especially during mid-latitude cyclones, impacts the dynamic and thermodynamic structure of the boundary layer and reduces extreme surface wind (Gentile et al., 2021; Varlas et al., 2017). In addition, recent studies have highlighted the significant potential for improved wind forecasting during windstorms taking into account the dynamic effects of waves (Lewis, Castillo Sanchez, Graham, et al., 2019; Wahle et al., 2017). A first approach for further studies is to couple the atmospheric model with a wave model. Furthermore, while surface latent heat exchange does not appear to be crucial for the development of rolls in windstorm Adrian, the impact of cloud microphysics on roll formation and wind transport might be relevant in other cases. Indeed, it has been shown that evaporative cooling can reduce the buoyancy of air parcels in windstorms, facilitating their descent to the surface and contributing to the amplification of surface wind gusts (Browning et al., 2015; Ludwig et al., 2015).

In this study, all available data, including in-situ observations and satellite images, are exploited to evaluate the different simulations. However, when it comes to winds at sea, these data prove insufficient. Measurements from buoys at sea are lacking in the region of strong winds, and would be useful for completing the validation of the simulations. Although LES provides detailed information on fine-scale processes, their evaluation is hampered by the lack of high-resolution observations. In this context, synthetic aperture radar satellite images have potential to reveal the details of roll vortices, as demonstrated by Brilouet et al. (2023) and Stopa et al. (2022). Such observation may constrain parameterizations of surface fluxes via their control on roll characteristics. Thus, the methodology of LES over a large domain developed here for the Mediterranean windstorm Adrian should be extended to other case studies. This would be essential to reach more general conclusions about the impact of air-sea fluxes on the roll morphology and the transport of strong winds to the surface.

## Appendix A: Description of the Surface Turbulent Flux Parameterizations

The COARE 3.0 (Fairall et al., 2003) parameterization, used in the reference simulations, belongs to the most commonly used bulk algorithm family stemming from the seminal Tropical Ocean-Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE; Fairall et al., 1996). These solve the transfer coefficients for heat and momentum iteratively based on the Monin and Obukhov (1957) similarity theory and eddy covariance measurements for wind speeds up to 25 m s⁻¹. New versions were released as new observations have become available. The intermediate version 3.0 used here was tuned to measurements up to 20 m s⁻¹ only. It gives slightly lower drag for wind speeds exceeding ≈18 m s⁻¹ but similar latent and sensible heat transfer coefficients than the later version COARE 3.5 (Edson et al., 2013). The difference in the drag coefficient stems from an updated wind speed dependence of the Charnock parameter αc (Charnock, 1955) used to account for wave effects on the roughness length. In COARE 3.0 αc equals 0.011 for winds up to 10 m s⁻¹ and 0.018 for winds over 18 m s⁻¹, increasing linearly in between.

WASP (Wave-Age Stress dependent Parameterization; Bouin et al., 2024) has the same iterative core as the COARE 3.0 and 3.5 algorithms. It differs in the Charnock parameterization, which is a piecewise function of wind and wave age that distinguishes four regimes: (a) for low wind speeds below 7 m s⁻¹ where wave age impacts are not considered, (b) for moderate wind speeds between 7 and 22 m s⁻¹ where wind sea growth leads to variability of the drag coefficient, (c) for high wind speeds from 23 to 45 m s⁻¹ where the drag coefficient decreases, wave breaking is dominant, and the dependence of the roughness on wave age is less important, and (d) for extreme wind speeds above 45 m s⁻¹ where the drag coefficient is held constant. In the first regime αc is only wind dependent. In the others αc is a power law of wave age with coefficients that are polynomial functions of the wind speed. The empirical coefficients of the piecewise αc parameterization were determined from the same eddy covariance data sets as those used for COARE 3.5 in the second regime, while for the higher regimes all available albeit less direct and likely less reliable data were used.
ECUME 6 is the latest version of Exchange Coefficient Unified Multi-campaign Experiments. This parame-
terization is developed and used operationally by Météo-France (Belamari, 2005). Contrary to the other algo-
rithms described above it parametrizes the scaled neutral exchange coefficients as a function of neutral 10-m
winds (in the absence of currents). There is thus no dependence of the transfer coefficients on the roughness length
or sea state through the Charnock parameter. Parameterizations of the neutral exchange coefficients are scaled on
a set of ship-borne eddy covariance measurements not considered for the other algorithms, as well as selected
extreme wind measurements of Powell et al. (2003), Donelan et al. (2004), and French et al. (2007) which suggest
saturation and decrease of the exchange coefficients for wind speeds higher than 30 m s⁻¹.

In the ANDREAS (Andreas et al., 2015) parameterization spray mediated latent and sensible heat fluxes are added to the interfacial bulk fluxes. The algorithm was tuned to flux measurements under up to 25 m s⁻¹ winds. Contrary to the COARE-type algorithms and similarly to the ECUME algorithm, there is no dependence of the friction velocity on the roughness length and Charnock parameter. The friction velocity is parameterized as a function of the neutral 10 m wind speed whereas the sea spray fluxes are computed from the bulk parameters and the friction velocity using the microphysical algorithm described in Andreas (2005). The contribution of spray to heat exchange becomes significant for wind speeds above 13 m s⁻¹.

Data Availability Statement

The codes used to analyze the data and prepare the figures are publicly available at Lfarh et al. (2024a). The
figures are created with Matplotlib version 3.3.4, available under the Matplotlib license (Caswell et al., 2021;
Hunter, 2007). The codes used to calculate auto-correlation functions have been developed by Granero Belinchon
et al. (2022) and are freely available at Belinchon (2022). In situ observations are available online via the
MeteoNet application of Météo-France (Larvor et al., 2020). All simulations were performed with the Meso-NH
model version 5.4 freely available under CeCILL-C license agreement (Lac et al., 2018). The meteorological
input data to create the initial and boundary conditions were retrieved through the ECMWF MARS server
(ECMWF, 2024). The model data are archived in the CALMIP and GENCI computing centers where they were
run. The whole data set exceeds 10 terabytes but subsets containing the data used to produce the figures are
available at Lfarh et al. (2024b).

Acknowledgments

Computer resources for running Meso-NH
were allocated by CALMIP through
project P20024 and GENCI through
project 0111437. This work was supported
by the French National Research Agency
under grant agreement ANR-21-CE01-
0002 and by COST Action CA19109. The
authors thank Carlos Granero Belinchon
for providing the auto-correlation tools and
for the discussions that contributed to the
elaboration of a part of the paper, as well as
Juan Escobar and Joris Pianezze of the
Meso-NH support team for their assistance
during this study. The authors also thank
three anonymous reviewers for their
comments that helped improve the paper.

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