# Using Computational Fluid Dynamics (CFD) to investigate airflow and sand transport on a human-made coastal foredune dominated by offshore wind: Impact of the shape variability.

Antoine Lamy, Thomas A.G. Smyth, Nicolas Robin, Patrick Hesp

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Antoine Lamy, Thomas A.G. Smyth, Nicolas Robin, Patrick Hesp. Using Computational Fluid Dynamics (CFD) to investigate airflow and sand transport on a human-made coastal foredune dominated by offshore wind: Impact of the shape variability. Coastal Engineering, 2024, 191, pp.104534. 10.1016/j.coastaleng.2024.104534. hal-04617949

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# Using Computational Fluid Dynamics (CFD) to investigate airflow and sand transport on a human-made coastal foredune dominated by offshore wind: Impact of the shape variability.

Antoine Lamy<sup>a, *</sup>, Thomas A.G. Smyth<sup>b</sup>, Nicolas Robin<sup>a</sup>, Patrick A. Hesp<sup>c</sup>

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## ARTICLE INFO

Keywords:

Air-flow dynamics

Aeolian sediment transport

Offshore wind

Dune management

## ABSTRACT

Foredunes provide many environmental and ecosystem services including protection from wave erosion and flooding hazards during storm events. While the impact of human interventions on the short-term evolution of coastal dunes is reasonably well understood, less is known about their contemporary influence on current wind and sediment dynamics several decades after implementation. The coastal dunes in Leucate (SE, France) have been anthropogenically constructed and are dominated by offshore wind conditions. Since their construction 20 years ago, a distinct variation in their longshore morphology has developed that is inherited from its original construction. The northern part of the dune has a symmetrical profile with a 28° degree stoss slope, 30° lee slope and a single crest. The southern part is asymmetric, with a gentler stoss slope (12°), 26° lee slope, and a double crest. To explore the potential geomorphic impacts of this distinct difference in morphology, several numerical simulations with varying wind speeds and direction were conducted. We used Computational Fluid Dynamics (CFD) to explore the spatial variations of the near surface wind flow, shear stress and aeolian sediment transport. **Results:** show that for each scenario, near surface wind speed accelerated toward the dune crest on the windward slope of the dune. The maximum wind speed varied with incident wind direction, the highest speeds occurring when incident wind flow was perpendicular to the dune crest. The double crest in the southern section of the dune affected the wind flow by inducing two consecutive speeds-up zones, with a greater maximum wind speed than on the single crested dune. Wind flow separation was observed where a steep lee slope was present (single crested dune), and only during perpendicular winds. This suggests that the shape of the dune and the direction of the wind are key parameters rather than wind speed. The area affected by reversed separated flow was spatially limited and did not extend beyond the dune toe but was below the threshold for aeolian sediment transport. Elsewhere in the lee of the dune, the wind was only deflected by an order of 15° for the oblique winds (310 and 330°), and less than 10° for the perpendicular wind (290°) on the southern part. In these locations, the shear velocity exceeded the threshold, notably on the southern dune, which coincided with the formation of undulating aeolian deposits in the lee of vegetation on the dune crest. The spatial differences observed in wind flow and aeolian sediment transport processes on this human-made dune were directly inherited from differences in their construction two decades ago. These results demonstrate the importance of the constructed dune profile, due to its potential impact on the long-term evolution of the landscape and the sediment budget of the system.

## 1. Introduction

Coastal sand dunes are one of the most important ecosystems in Europe, hosting a wide range of fauna and flora (Martínez and Psuty, 2004; Acosta et al., 2009; Marcenò et al., 2018; Laporte-Fauret et al.,

2021) which include several endemic species (van der Maarel and van der Maarel-Versluys, 1996; Van der Maarel, 2003). They are also an efficient natural coastal defence during storm events and have a key role in protecting inland regions from flooding. However, coastal areas are a heavily anthropogenically exploited environment with tourism and

<footnote><sup>a</sup> CEFREM, UMR, CNRS 5110, Université de Perpignan Via-Domitia, 66100, Perpignan, France</footnote>

<footnote><sup>b</sup> Department of Biological and Geographical Sciences, School of Applied Sciences, University of Huddersfield, England, United Kingdom</footnote>

<footnote><sup>c</sup> Beach and Dune Systems (BEADS) Laboratory, College of Science and Engineering, Flinders University, Bedford Park, South Australia, 5041, Australia</footnote>

<footnote>* Corresponding author.
E-mail address: antoine.lamy.1@univ-perp.fr (A. Lamy).</footnote>
residential uses resulting in ecosystem loss and beach-dune degradation (Hesp and Martínez, 2007; Malavasi et al., 2016; Delgado-Fernandez et al., 2019; Robin et al., 2021). Consequently, coastal dunes in Europe have lost 25% of their extent in 1998, compared to 1900 (Delbaere, 1998) and 75% of Mediterranean coastal dunes have been damaged or destroyed (Géhu, 1985; Salman and Strating, 1992).

Globally, a trend toward coastal dune stabilisation due to an increase in vegetation cover has been observed in the last century. This “greening” may be due to the combined effects of climatic change (e.g., increasing temperature, precipitations, atmospheric nutrients and reduced windiness) and anthropogenic pressure (Jackson et al., 2019; Gao et al., 2020). In many parts of the world, coastal dune stabilisation has been initiated by human actions such as fencing, vegetation planting or reshaping the dune profile to counteract erosion (Nordstrom and Arens, 1998; Arens et al., 2001; Matias et al., 2005; Ruz and Anthony, 2008; Hesp and Hilton, 2013; Hacker et al., 2019; Itzkin et al., 2020a; Robin et al., 2021). In several places, sand structures on the back beach, that are commonly referred to as “dune dykes” have also been built to protect inland areas (Perk et al., 2019; Derijckere et al., 2023; Rauwoens et al., 2023). In some cases, these artificial dunes have been constructed with fabricated cores e.g. geotextile tubes (Harris and Ellis, 2020; Maximiliano-Cordova et al., 2023). The impact of these artificial dune stabilisation methods is generally perceived as positive in terms of influence on the sediment budget of the system contemporary to their construction (Itzkin et al., 2020a, 2020b; Derijckere et al., 2023; Rauwoens et al., 2023). Much less is known about the geomorphic evolution of these dunes several years after their construction.

Dune systems evolve through interactions and feedbacks between fluid flow, bed morphology and sediment transport (Best, 1993; Arens et al., 2001; Walker and Nickling, 2002; Bauer et al., 2022; Hesp and Walker, 2022; Walker et al., 2022). The recent development of Computational Fluid Dynamics (CFD) to model wind flow over aeolian landforms, has led to a more holistic understanding of these systems (Smyth, 2016). In particular, sand dune morphology has a dramatic influence on boundary layer flow and resulting sediment transport (Hesp and Smyth, 2019b). As near surface winds move up the stoss slope of a dune, they become steered perpendicular to the crest and accelerate in speed, accompanied by an increase in shear stress and sediment transport (Walker and Nickling, 2002; Hesp et al., 2005, 2015; Bauer et al., 2012; Walker and Shugar, 2013; Davidson et al., 2022). In the lee of the dune crest, flow expansion and deceleration occur, and a low-pressure zone on the lee side of the dune creates an area of detached, separated flow. It is characterized by flow reversal when the incident wind is perpendicular to the dune crest (Sweet and Kocurek, 1990; Walker and Nickling, 2002; Parsons et al., 2004; Jackson et al., 2011; Bauer et al., 2012; Delgado-Fernandez et al., 2013; Jackson et al., 2013; Hesp and Smyth, 2016a; Davidson et al., 2022). This secondary flow in lee of the dune crest is controlled by both dune morphology and wind direction. The higher the dune and the steeper the lee-side slope, the more likely separated flow will transport sediment across and downwind of the lee slope (Sweet and Kocurek, 1990; Walker and Nickling, 2002; Parsons et al., 2004; Walker et al., 2006; Lynch et al., 2009, 2010; Bauer et al., 2012, 2015; Hesp and Smyth, 2019a; Bauer and Wakes, 2022) and the more oblique the incident wind direction, the less likely flow separation will occur (Sweet and Kocurek, 1990; Bauer et al., 2012; Delgado-Fernandez et al., 2013; Walker and Shugar, 2013; Hesp et al., 2015; Hilton et al., 2016; Hesp and Smyth, 2019b; Davidson et al., 2022). Patterns of separated, reversed and deflected flow play a key role in dune evolution, particularly during offshore winds. This is due to the potentially seaward export of sand from the beach-dune system to shallow water in the swash zone. However, when wind flow separation and reversal occurs, sediment may instead nourish the back beach and dune toe, rather than be moved offshore (Lynch et al., 2009, 2010; Bauer et al., 2012, 2015; Delgado-Fernandez et al., 2013; Nordstrom and Jackson, 2018). Due to the dominance of onshore winds in coastal areas, less attention has been devoted to offshore wind flows by in-situ

measurements, (Gares et al., 1993; Sabatier et al., 2002; Lynch et al., 2009; Jackson et al., 2011; Delgado-Fernandez et al., 2013; Kaplan et al., 2016; Nordstrom and Jackson, 2018; Lamy et al., 2024b) or CFD simulations (Jackson et al., 2011) despite their prevailing nature on many coasts.

The purpose of this study is to investigate for the first time wind flow and sediment transport dynamics on an anthropologically constructed dune, dominated by offshore wind conditions. The field site (Leucate, North-West Mediterranean coast) is a dyke built 20 years ago, in 2004, characterized by heterogeneous longitudinal morphology. Since its construction it has been left to evolve naturally. The results focus on wind flow and sediment transport dynamics across the human-made coastal dune, to better understand the influence of inherited anthropic morphology on beach-dune geomorphology.

## 2. Study site and methods

### 2.1. Study site

The study site is located at Leucate Beach in the South of the Gulf of Lion on the French Mediterranean coast (Fig. 1). It is a microtidal and wave-dominated environment (Aleman et al., 2011). The tidal range is small (0.3 m at mean spring tide) but larger variations can occur during marine storms. The combined action of high speed winds, large waves and low atmospheric pressure, allows wave set-up to reach 1 m near the shoreline (Certain, 2002). The mean significant wave heights ($H_s$) are small ($H_s < 0.3$ m for 75% of the time and $H_s < 1.5$ m for 94%) but during winter storms the $H_s$ can be above 4 m (Aleman et al., 2015). The site is dominated by two wind orientations (Feyssat et al., 2023). NW offshore wind 71.5% of the time ($17.5 \% \ge 10$ m/s between 2015 and 2022) and E to SE onshore winds (28.5% of the time with 22% of the time $\ge 10$ m/s) (Fig. 1a). The persistent offshore winds are a result of global climatic circulation patterns in the North Atlantic and Western Europe. This creates a pressure gradient in the Gulf of Lion which induce offshore winds, as well as the sites position between two mountain chains (the Pyrenees and the Central Massif), resulting in a higher wind intensity caused by the Venturi effect. This pattern results in the dominance of fast, and dry offshore winds predominantly between autumn and spring, with wind gusts up to 28 m/s for 10–30 days per year and a peak maximum wind speed of more than 40 m/s. The fastest onshore winds are more frequent in winter, and they are combined with high air humidity, rainfall and high wave energy (Feyssat et al., 2022).

Leucate Beach is a narrow coastal barrier (1.8 km long and 0.5 km wide) that closed the Leucate lagoon at 2000 BP (Certain, 2002). The mean beach width is around 40–50 m with a flat relief and a low elevation (1 m NGF, French Ordnance Datum in which 0 is close to mean sea level). The dune system is composed of a single foredune that runs north to south, with a maximum elevation around 4.5 m NGF and a width around 7–15 m (Fig. 1). The crest is flattened by a footpath. The stoss slope and the landward dune crest are vegetated and are backed by a flat area (Fig. 2). Before the 1970s the coastal barrier was flat and connected to the lagoon with multiple inlets (Fig. 1c). Between the 1970s to 2004 a road crossed the barrier from North to South at the current position of the dune. This road was initially used to build the town of Port-Leucate southward, then it was used as access to the beach for tourism. In 2004, the road was closed and progressively deconstructed. The excavated materials were used to build a stone mound (Fig. 1d) which constitutes the core of the southern part of the dune. In the following years, this mound has been filled with sand from harbour dredging and gradually covered by vegetation which has fixed the dune in place. Although the longshore maximum elevation of the dune crest is relatively constant, the dune presents two different morphologies due to differences in construction. The southern part is composed of two straight lines of rocks filled with dredged sand (named dredge and rock core profile in this study), whereas the north part is constructed from only dredged sand (named dredged material profile in this study).
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Wind characteristics at the meteorological station at cape Leucate from 2015 to 2022. (b) field photography in the south part of the dune with undulated aeolian landform and the lee (seaward) side of the dune. (c), (d) and (e) Evolution of the study site by aerial photography, from natural in 1943, rock dune in 2003 to the actual sand dune filled by dredging sand for its south part and completely built with dredging sand for its north part.</figcaption></figure>

(Fig. 2). The southern dune is characterised by two crests with the seaward crest being the tallest. The south part of the dune also contains a sequence of topographic undulations due to sediment deposition behind stands of vegetation on the dune crest. They extend down the lee side slope (Figs. 1b and 2), oriented in the main north-west offshore wind direction (310°).

## 2.2. Field acquisition

Wind data was collected in the field on the 17th of January 2023

during an offshore wind event. Nine ultrasonic anemometers (GILL WindSonic 4) were positioned on a cross-shore profile at 0.3 m above the bed surface (p1, Fig. 2) sampling at 1 Hz, which was then averaged at 1-min intervals. A detailed topographic map of the study site was made on the 20th of March 2023 with a LiDAR (Riegl VQ-780i) mounted on a helicopter. The accuracy of the data is below 0.2 m (XYZ) and was be used to generate a Digital Elevation Model (DEM) of the field site. The comparison between topographic profiles (DGPS-RTK) of January 2023 and the LiDAR of March 2023 does not show any significant evolution of the field site.
<figure><img src="image_5.png" /><figcaption>Fig. 2. Topographic LiDAR of the field site, the circles represented the undulated forms on the lee side of the southern part. The dashed lines showed the localisation of the rock line inside the dune.</figcaption></figure>

## 2.3. Computational fluid dynamics methods

### 2.3.1. Computational fluid dynamics model

Wind flow modelling was performed using the open-source computational fluid dynamics (CFD) software OpenFOAM® developed primarily by OpenCFD Ltd. since 2004. Flow was modelled as an incompressible fluid using the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm and the Reynolds-Averaged Navier-Stokes (RANS) equations, which produced a steady-state time-averaged solution. Turbulence was modelled by the Re-Normalised Group (RNG) k-ε model which has been successfully validated to simulate air flow in a range of coastal dune environments (Jackson et al., 2011, 2020; Smyth et al., 2012, 2013; Hesp et al., 2015; Hesp and Smyth, 2016; Nguyen et al., 2022).

### 2.3.2. Computational domains

A DEM of the LiDAR acquisition was used as the surface of the computational domain, with the OpenFOAM tool snappyHexMesh used to generate a mesh of the study site. The computational domain measured 120 m long × 100 m wide × 52 m in height, to ensure that the modelled wind flow was sufficiently well-developed at the two study locations and wasn't impacted by edge effects at the extremities of the computational domain (Franke et al., 2007). The computational domain cell size decreased gradually from the upper boundary (2.5 × 2.5 × 2.5 m) to the surface (0.3 × 0.3 × 0.15 m) and was more than 3 million cells in total.

### 2.3.3. Boundary conditions

The computational domain was divided in two parts to better represent the surface roughness lengths ($z_0$) present in the field. Landward of the dune crest was vegetated and thus prescribed a $z_0$ of 0.07 m (Sutton, 1953). Seaward of the dune crest, the surface was composed of sand and thus a $z_0$ of 0.0005 m was applied (Bagnold, 1960). In addition, data (hourly maximum gust and mean wind) from a Météo-France meteorological station located at Cape Leucate (3 km north of the study area, 10 m height) was used to define the main occurrences of offshore wind speed and direction value from 2015 to 2022. These values informed the prevailing wind characteristics for the CFD. During the offshore windstorms, wind gusts exceeded 15 m/s more than 30% of the time and 20% of the mean wind speeds were above 15 m/s. Wind gusts also exceeded 25 m/s more than 3% of the time and wind direction ranged from perpendicular offshore (290°) to oblique offshore (310° and 330°). As a result, wind speed at the inlet of the domain was set at 15, 20 and 25 m/s at 10 m above the surface at the inlet boundary at wind directions of 290°, 310° and 330°. At the inlet boundary of the CFD model, wind speed ($U$), turbulent kinetic energy ($k$) and energy dissipation ($\epsilon$) were defined using Eqs. (1)–(3), (Richards and Hoxey, 1993).

$$U(z) = \frac{u_*}{\kappa} \ln \left( \frac{z + z_0}{z_0} \right) \qquad (1)$$

$$k(z) = \frac{u_*^2}{\sqrt{C_\mu}} \qquad (2)$$
$$ \epsilon(z) = \frac{u_*^3}{\kappa(y + y_0)} \qquad (3) $$

where $U(z)$ is the wind speed at height $z$, $u_*$ is shear velocity, $\kappa$ is the Von Karman constant (0.4187) and $y_0$ is the surface roughness length. where $C_\mu$ is a constant of the $k-\epsilon$ model and equals 0.09.

### 2.3.4. Modelled aeolian sand transport

The sand transport flux was calculated over the computational domain using the Lettau and Lettau (1977) equation Eq. (4):

$$ q = C \sqrt{\frac{d}{D}} \frac{\rho}{g} (u_* - u_{st}) u_*^2 \qquad (4) $$

where $q$ is sand flux in kg/m/s, $C$ is an empirical constant equal to 4.2, $D$ is the reference grain diameter, 0.25 mm, $d$ is grain size in mm, $\rho$ is the air density, 1.2466 kg/m³, $g$ is gravity in m/s², $u^*$ is shear velocity in m/s and $u_{st}$ is threshold shear velocity in m/s, calculated by Eq. (5) as 0.40 m/s in this study with $\rho_s$ the sediment density, 2 650 kg/m³ and $d$ the beach grain size, 0.750 mm. Based on the work of Smyth and Hesp (2015), the shear velocity ($u^*$) was calculated at the surface of the CFD domain using the shear stress $\tau$ (m²/s²) using Eq. (6).

$$ u_{st} = A \sqrt{\frac{\rho_s - \rho}{\rho}} gd \qquad (5) $$

$$ u_* = \sqrt{\left(\frac{\tau}{\rho}\right)} \qquad (6) $$

### 2.3.5. Comparison between observed and CFD modelled winds

During the measurement campaign, 4 h of wind were recorded at 1 Hz then averaged to 1 min, which has been deemed an appropriate

averaging interval to represent wind and sand transport (Baas and Sherman, 2006; Davidson-Arnott et al., 2012; Smyth et al., 2009; Smyth et al., 2014). The standard deviation (SD) and the coefficient of variation (CV) were calculated as an indicator for wind flow variability Eq. (7) (Walker et al., 2009; Smyth et al., 2014).

$$ CV = \frac{SD}{mean} \qquad (7) $$

The CFD gives a steady state result for one initial value of wind speed and direction. To be comparable with the field observations, the average observed wind with the lowest wind fluctuation (lowest CV) has been chosen. This choice ensures having the best representation of the observed averaged value, with the least possible fluctuation of the incident wind. For the validation case, the modelling incident wind flow was set at 17 m/s and 292° on the inlet of the computational domain at 10 m above the surface. As the observed wind was recorded at 0.3 m high the extracted results of the CFD were taken at the same altitude. Overall, the CFD results compare well with measured wind speed and direction, ($r^2$ = 0.93 for the wind speed and 0.98 for the direction). For the wind speed, the greatest difference between the field and the CFD results are at stations 3 and 4 where the wind speed was underpredicted by 26% (1.9 m/s) and 32% (0.4 m/s) respectively). As observed by Smyth et al. (2012, 2013), these differences occur at the areas with the greatest wind flow variability. Regarding wind direction, the greatest discrepancy was from the lee slope to the berm crest (from station 5 to 9) with a variance around 5 %. Nevertheless, the modelled wind showed a good agreement with the field data and matched the wind recirculation on the lee side of the dune (Fig. 3).

<figure><img src="image_6.png" /><figcaption>Fig. 3. Comparison of wind speed and wind direction between 1-min averaged field data and the simulation using CFD on a cross-shore profile. The wind characteristics showed by the arrows represent a plan view of the wind direction.</figcaption></figure>
# 3. Results

## 3.1. Air flow dynamics from the back dune to the dune crest

The results of the wind flow modelling are presented as planimetric maps of the computational domain as well as two cross-shore transects. The northern profile crosses the part of the dune made by dredging material only (North part, p1) and the second profile crosses the dune constructed with a rock core and dredged material (South part, p2). These results were shown with Figs. 4–6. In all modelled scenarios, wind speed and direction above the back dune remained the same as incident conditions. As wind flow approached the dune, on the north part (p1), a slight deceleration (about 1 m/s) was observed at the toe of the stoss slope, which increased as the incident wind became increasingly perpendicular to the dune crest. On the stoss slope, an acceleration of the wind was observed reaching its maximum at the crest (Panels d and e on

the “landward part” in Figs. 4–6). Wind speed at the crest increased as wind direction became more perpendicular to the crest. Patterns of wind flow were not uniform along the dune, however. On the north part of the dune (p1) the acceleration occurred as a single peak. For the oblique winds, the wind was accelerated by a factor 1.6 and 1.8 respectively for the 310° and 330° simulations compared to the wind speeds 5 m upwind of the dune. For the perpendicular wind, this speedup factor was close to 2 (Fig. 4d, 5d and 6d). The southern part (p2) was characterized by two peaks in wind speed. One is observed on the landward crest and the other on the seaward crest, with a slightly higher acceleration than on p1 by 1 m/s up to 2 m/s for the perpendicular wind (Fig. 4d, 5d and 6d). For the oblique winds, the speeds at dune crest increased by a factor of 1.8–2.1. For the wind perpendicular to the crest, it was 2.3 times faster than the wind upstream of the dune (Fig. 4e, 5e and 6e). Between the two speed-up peaks at p2, a sudden deceleration of the wind, consistent irrespective of the different wind speeds and directions modelled, was

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Wind speed 0.3 m above the surface for a 15 m/s incident wind speed at 290° (a), 310° (b) and 330° (c). Profile p1 and p2, representing the crossshore variation of the wind characteristics (d and e) on the two different dune shape profiles (dashed line).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Wind speed 0.3 m above the surface for a 20 m/s incident wind speed at 290° (a), 310° (b) and 330° (c). Profile p1 and p2, representing the crossshore variation of the wind characteristics (d and e) on the two different dune shape profiles (dashed line).</figcaption></figure>

observed where the footpath is present. For each simulation, directional steering of about 15° towards crest normal for the oblique winds occurred. This behaviour was especially prominent on p1 for the oblique winds which had a more uniform stoss slope.

## 3.2. Air flow dynamics from the dune crest to the beach

Once the maximum dune elevation is crossed, the behaviour of the air flow differed according to the two different dune shapes. For the northern profile (p1), the wind speeds decreased firstly on the top of the dune then on the lee side. The intensity of wind flow deceleration was strongly controlled by incident wind flow obliquity, reaching the lowest wind speeds during perpendicular winds where it was close to 0 m/s at the dune toe (Fig. 4d, 5d and 6d). Downwind of the dune toe, wind speeds accelerated before reaching a maximum on the crest of the beach berm. With regards to wind flow directional steering in the lee of the

dune crest, wind flow was deflected crest parallel for the oblique winds, to a greater extent on the northern dune profile compared to the south (Panels d and e on Figs. 4–6). Regarding the perpendicular 290° incident winds, at the northern single crested dune profile, wind flow became separated and reversed in the lee slope and dune toe area, with a rapid reattachment after the dune toe (Panels a and d on Figs. 4–6). Due to a different morphology at the crest of the dune at p2, deceleration only occurred above the downslope in lee of the dune crest. It remained relatively high at the dune toe, with values above 6, 8 and 10 m/s, respectively, for the incident modelled wind speeds of 15, 20 and 25 m/s at 10 m above the surface (Panels e on Figs. 4–6). While the cases with an incident wind direction of 290° and 310° showed a comparable deceleration on the lee slope to the dune toe and a gradual acceleration across the beach (Panels a, b and e on Figs. 4–6). The most oblique simulated wind (330°) had a lower deceleration and a higher wind speed on the whole beach profile (Panels c and e on Figs. 4–6).
<figure><img src="image_9.png" /><figcaption>Fig. 6. Wind speed 0.3 m above the surface for a 25 m/s incident wind speed at 290° (a), 310° (b) and 330° (c). Profile p1 and p2, representing the crossshore variation of the wind characteristics (d and e) on the two different dune shape profiles (dashed line).</figcaption></figure>

### 3.3. Shear velocity and aeolian sand transport

The results of shear velocity and sand transport in the offshore direction are only described leeward of the dune crest, as this part of the dune and the beach was the most susceptible to sand transport as it was not covered by vegetation (Fig. 1b). Shear velocity followed the same spatial pattern as wind speed with a gradual increase from the lee of the dune to the lower beach. However, several particularities can be noted. On the lee slope and dune toe of the northern profile, there was a significant variation in shear velocity values among the different simulation scenarios. From close to 0 m/s for the 290° and 15 m/s simulation (Fig. 7d), to close to 1 m/s for the 330° and 25 m/s simulation (Fig. 9d). The threshold shear velocity (0.40 m/s) was rarely or only marginally reached except during high incident wind speeds (25 m/s) and/or oblique wind conditions (Fig. 7c and d, panels b, c and d on Figs. 8 and 9). These differences decrease with distance from the dune toe and the

shear velocity from the 310° and 290° simulations were quite similar near the berm crest for all wind speeds (Panels a, b and d on Figs. 7–9). At the lee slope and dune toe of the southern profile, the shear velocity was higher and always above the threshold. Thus, potential sand transport on the lee slope and dune toe region was greater on this part of the dune. But these differences decreased moving away from the dune and the transport rates were quite similar on the berm. For all simulations, threshold shear velocity was surpassed on the beach (Panels a, b and c on Figs. 7–9) and sediment flux increased gradually from the dune toe to the sea. Highest fluxes were modelled when incident winds were at their most oblique (Panels d and e on Figs. 7–9).

## 4. Discussion

This study was not intended to discuss the validity of the CFD calculations by comparing it with field observations. Nevertheless, as wind
<figure><img src="image_10.png" /><figcaption>Fig. 7. Surface Shear velocity for a 15 m/s incident windspeed at 290° (a), 310° (b) and 330° (c), the grey colour on the dune lee side showed the under-threshold shear velocity zone. The two crossshore profiles p1 and p2 showed the shear velocity and sand transport on the dune lee side and beach (d and e).</figcaption></figure>

flow dynamics in coastal environments are complex, it is valuable to directly compare modelled wind flow with field measurements (Wakes et al., 2005; Smyth et al., 2012, 2019; Wakes, 2013; Hesp et al., 2015; Hilton et al., 2016; Nguyen et al., 2021). This has been done successfully in this study (Fig. 2) and strengthened the relevance of the results, and, overall, the use of CFD in coastal environments.

## 4.1. Relationship between dune shape, air flow and sediment transport pattern

In this study, although shear velocity was used to calculate the sediment transport rate, it was obtained using CFD rather than the traditional technique of deriving shear stress from a regression of a vertical wind profile (Jackson et al., 2020; Smyth and Hesp, 2015). However, the modelled aeolian sand transport values remain an estimation of the patterns of sand flux with different incident wind conditions. Further research must be done to compare the modelled sand flux using this method, with observed aeolian sand flux in order to permit the quantitative use of these results. Nevertheless, the simulations in this study correlate with the findings of measured data from Lamy et al. (2024a) at the same site, who found that sediment flux increased on the beach downwind of the dune crest.

### 4.1.1. Stoss side patterns

Results from the CFD modelling demonstrated that wind flow

became steered crest perpendicular above the stoss slope, consistent with measurements and observations made by Walker et al. (2006); Lynch et al. (2009); Hesp et al. (2015); Hilton et al. (2016); Davidson et al. (2022). Flow deflection of approximately 15° occurred during 20° and 40° to shore-normal incident winds, for the perpendicular winds the deflection was below 10°. Wind flow speed-up was also observed above the stoss slope of the dune reaching a maximum at the dune crest as observed by Hesp et al. (2005). Due to morphological differences in the dune shape, the southern section had two peaks of high wind speed. They were slightly faster than the maximum wind speed recorded on the single peak of the northern dune. Because the dune crest is almost the same height for both profiles, this observation can only be explained by the presence of the double crest.

### 4.1.2. Lee side pattern

The occurrence of separated and reversed airflow in the lee of foredunes and transverse dunes has been described in multiple studies (e.g., Walker and Nickling, 2002; Bauer et al., 2012; Delgado-Fernandez et al., 2013; Davidson et al., 2022). In this study, wind flow separation was observed in lee of the dune crest but only when incident winds were perpendicular to the crest and only on the northern part of the dune (p1). The development of separated flow with perpendicular wind is consistent with previous literature (Sweet and Kocurek, 1990; Lynch et al., 2010; Jackson et al., 2011; Delgado-Fernandez et al., 2011; Hesp et al., 2015; Hesp and Smyth, 2019b) as oblique winds effectively
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Surface Shear velocity for a 20 m/s incident windspeed at 290° (a), 310° (b) and 330° (c), the grey colour on the dune lee side showed the under-threshold shear velocity zone. The two crossshore profiles p1 and p2 showed the shear velocity and sand transport on the dune lee side and beach (d and e).</figcaption></figure>

'flatten' or 'shallow' the stoss slope profile (See Fig. 1 in Hesp and Smyth, 2016a). The impact of stoss slope steepness also helps explain the difference in wind flow separation in profiles 1, where flow separation was present and 2, where wind flow separation was absent. The northern section of the dune (p1) had relatively steep stoss (28°), and lee (30°) slopes compared to southern part of the dune (p2) (12° and 26° respectively). Consequently, the shear velocity in the lee of the dune (p1) was very low (under the threshold (<0.40 m/s)). It could not induce sediment transport towards the dune despite the existence of wind flow reversal and strong incident winds. On the southern part of the dune, the flow was not separated but only slightly deflected. Here shear velocity remained above threshold velocity and perpendicular winds allowed sediment transport on the lee side away from the dune crest. The pattern of the flow separation region under offshore winds was the same whatever the wind speed simulations. It means that the occurrence of separated and reversed flow does not depend of the wind speed (Hesp et al., 2005; Smyth et al., 2013; Smyth and Hesp, 2015) but on the wind direction and dune shape (Sweet and Kocurek, 1990; Parsons et al., 2004; Lynch et al., 2010; Delgado-Fernandez et al., 2011; Hesp and Smyth, 2019b). To the best of the authors knowledge, all the studies analysing the presence of separated and reversed air flow on the lee of coastal sand dunes, have been conducted on dunes substantially taller (5–15 m) and wider (>40 m) than those examined in this study (2.5 m in height and 10–15 m in width) (e.g. Lynch et al., 2010; Delgado-Fernandez et al., 2011; Bauer et al., 2012; Delgado-Fernandez et al.,

2013; D. W. T. Jackson et al., 2013; Davidson et al., 2022). This study highlights that even relatively small dunes can have a substantial impact on secondary wind flow dynamics on the back beach. For oblique incident winds in this study, deflected rather than separated flow was observed in lee of the crest and thus sediment transport was alongshore in the direction on the lee slope and dune toe as described in Walker and Nickling, 2002; Lynch et al. (2009); Bauer et al. (2012); Walker and Shugar (2013). However, the behaviour affecting the lee side air flow and sediment transport during these wind conditions was spatially (north/south) different due to the variability of the dune shape. The double crest of the southern part created higher wind speeds on the crest immediately upwind of the lee slope. Consequently, the shear velocity gets higher in this part of the system and the oblique winds were strong enough to transport, and then deposit, more sediment on the lee slope. This mechanism explained the occurrence on the southern part of discrete sand tongues and depositional bedforms (Fig. 10). That were not present or poorly developed on the northern part where upwind sediment supply was identical (uniformly covered by vegetation and with a flat topography). Instead, the sediment source for these small 'sand tongues' could be the local bare sand patches just upwind of the dune crest (Fig. 10b), or remobilisation of sand from the top of the lee slope. The obliquity of these bedforms matches the orientation of the main offshore wind direction at the field site (35% of the time at 310°), suggesting that this wind direction was likely responsible for these landforms.
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Surface Shear velocity for a 25 m/s incident windspeed at 290° (a), 310° (b) and 330° (c), the grey colour on the dune lee side showed the under-threshold shear velocity zone. The two crossshore profiles p1 and p2 showed the shear velocity and sand transport on the dune lee side and beach (d and e).</figcaption></figure>

## 4.2. Impact and lessons of dune design

To protect the Leucate coastal barrier from flooding, an artificial dune was created two decades before this study took place. The shape was not based on an understanding of the aeolian sediment transport processes on this coast which are dominated by offshore winds but on basic experimentation. The north part of the dune was exclusively made from dredged materials and has a more symmetric shape with a steep stoss and lee slope (p1) (Fig. 2). The southern part was made with two straight rock lines then covered by dredged sand, which created a double crested dune, with shallower slope gradient and an asymmetrical shape. Since its construction, the Leucate dune was quickly fixed by a high density of vegetation (natural) and has evolved with concomitant mixing of natural and anthropogenic (eroded crest dune by a footpath) processes. In this study, the dynamics of the dune was investigated only by studying the offshore wind pattern, since offshore winds dominate the regional wind field. It is likely that onshore winds would result or have resulted in some foredune building or initiation in the long term, but these occur only occasionally. Onshore winds are commonly accompanied by rainfall and high waves (Feyssat et al., 2023), restricting the potential aeolian sand transport. Marine storms reach the dune toe only during periods when Hs > 4 m (Lamy et al., 2024b), and this condition occurred only 12 times between January 2006 to December 2022, for example, so dune erosion is not significant.

The lasting geomorphological imprint of the differences in dune construction on the contemporary landscape underline the fact that dune morphology can be inherited from the past. This is consistent with Robin et al. (2021), who observed the influence of fences and reshaping on the landscape of the Truc Vert dune (Aquitain coast, France) since the 1860's. Bossard and Nicolae Lerma (2020) also observed that the majority of foredunes on this coast maintain the “engineered profile” originated from their construction almost 40 years before. Thus, reflection on the type of dune profile constructed is crucial in view of the long-term morphological consequences that this generates. This is even more important in regions where colonisation by vegetation can be rapid because of vegetation planting or in relation to the actual trends in dune greening. The result could be a stabilisation of artificial dune shape instead of a more natural evolution of these types of engineered dune profile (Jackson et al., 2019; Gao et al., 2020). Numerical simulations by CFD illustrated the impact of the two different morphologies on the wind flow patterns and the shear stress which, in turn, influenced the topographic evolution of the beach-dune system. For example, the dune's shape and height does not allow the development of enough airflow reversal to result in sediment transport from the back beach toward the dune toe. Unlike previous studies over taller dunes who observed foredune accretion during offshore winds (Lynch et al., 2009, 2013). Moreover, the morphology of the dune also does little to prevent sand from being exported from the beach to the shallow water. However, a
<figure><img src="image_13.png" /><figcaption>Fig. 10. (a) zoom on the undulated landforms (circled in red) on the shear velocity map (Incident wind at 310° and 20 m/s). (b) undulated landforms on the field.</figcaption></figure>

beneficial effect of the created dune shape is the formation of deposi-
tional landforms on the lee slope of the southern dune (Figs. 7b, 8b and
9b, Fig 10). Because of the initial design of the southern dune, the actual
dune shape allows sand transport and deposition, at, and beyond the
dune crest. As the size of the dune is limited, these landforms are rela-
tively small. In a larger scale environment, they could provide additional
protection for the dune toe during marine storms as they generate a
slightly elevated topographic profile. Thus, the results of this study
demonstrate the influence of historical anthropogenic dune design on
contemporary dune morphology by the occurrence of the landforms in
the southern dune. But in addition, this influence also effects long-term
morphological evolution, as demonstrated by the alongshore shape of
the dune being different (Fig. 2). Nevertheless, the long-term morpho-
dynamical development of the dune in this study remains limited
regarding to the coastal defence provided. On a larger scale dune system,
this long-term evolutionary pattern could be exacerbated and eventually
influence the effectiveness of the coastal protection provided.

5. Conclusion

This study modelled air flow and resultant sediment transport over a
human-made dune that varied morphologically alongshore due to the
methods used in its construction. The northern part of the dune was built
from dredged sand only, while the southern part was constructed with a
rock core and then filled with dredged sand. These differences in the
dune engineering have created two models of dune morphology which
impact contemporary wind flow dynamics and aeolian sediment trans-
port. The following conclusions can be derived from this study:

1. Dune construction methods potentially impact geomorphological processes decades after construction. In this study, the potential imprints of two different construction methods on the wind flow and

sediment transport processes at the same site are still present after 20
years of dune construction.

2. Additional planning is recommended when constructing artificial dunes, particularly with the end goal in mind. As with the small dune studied here, certain constructed morphologies could lead to a varying dune shape affecting aeolian sand processes. On larger constructed coastal dunes, the relatively small changes observed here could be exacerbated. This could have a significant impact on the services provided by the created dune.

3. This study has shown that secondary wind flow patterns can exist even over relatively small dunes (2.5 m high and 10–15 m width) and have substantial impacts of sediment transport on a beach, particularly during perpendicular offshore winds.

4. The pattern of wind flow perturbation (speed up and wind steering) above the dune depends on dune shape and wind direction rather than the wind speed. These patterns of secondary wind flow impact sediment transport in lee of the dune crest, which increases on the beach with distance from the dune. However longshore variation on this sediment transport exists, caused by longshore morphological variation of the dune.

This study also highlighted the effectiveness of CFD as a tool to
accurately reproduce near surface air flow dynamics, even in the case of
a small and highly modified dune system. Future research will aim to
examine the efficiency of aeolian sediment transport rates, calculated by
deriving the near surface shear stress from the surface of the computa-
tional domain in comparison to observed transport rates. This validation
would enable more quantitative use of sediment flux derived in this
manner which will lead to a better understanding of the longshore
sediment transport fluctuations on the beach under offshore winds.
CRediT authorship contribution statement

**Antoine Lamy:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation, Conceptualization. **Thomas A.G. Smyth:** Writing – review & editing, Software, Methodology, Formal analysis, Conceptualization. **Nicolas Robin:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Conceptualization. **Patrick A. Hesp:** Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgements

The authors thank Obscat and the Parc Naturel Marin du Golfe du Lion for their financial support. The corresponding author is funded through a ministerial PhD grant from the French government. This study has been partially supported through the grant EUR TESS N°ANR-18-EURE-0018 in the framework of the Programme des Investissements d'Avenir. The authors would like to thank the editor-in-chief, N. Cohn and anonymous reviewer who helped to improve this article. The authors thank Météo-France for supplying meteorological data and all the contributors to the fieldwork.

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