Effects of Waves on Coastal Water Dispersion in a Small Estuarine Bay M

JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 119, 1–17, doi:10.1002/2013JC009466, 2014

Effects of waves on coastal water dispersion in a small estuarine bay M. T. Delpey,1 F. Ardhuin,2 P. Otheguy,1 and A. Jouon1 Received 27 September 2013; revised 2 December 2013; accepted 9 December 2013.

[1] A three-dimensional wave-current model is used to investigate wave-induced circulations in a small estuarine bay and its impact on freshwater exchanges with the inner shelf, related to stratified river plume dispersion. Modeled salinity fields exhibit a lower salinity surface layer due to river outflows, with typical depth of 1 m inside the bay. The asymmetric wave forcing on the bay circulation, related to the local bathymetry, significantly impacts the river plumes. It is found that the transport initiated in the surf zone by the longshore current can oppose and thus reduce the primary outflow of freshwater through the bay inlets. Using the model to examine a high river runoff event occurring during a high-energy wave episode, waves are found to induce a 24 h delay in freshwater evacuation. At the end of the runoff event, waves have reduced the freshwater flux to the ocean by a factor 5, and the total freshwater volume inside the bay is increased by 40%. According to the model, and for this event, the effect of the surf zone current on the bay flushing is larger than that of the wind. The freshwater balance is sensitive to incident wave conditions. Maximum freshwater retention is found for intermediate offshore wave heights 1m< Hs < 2 m. For higher-energy waves, the increase in the longshore current reduces the retention, which is two times lower for Hs 5 4 m than for Hs 5 2m. Citation: Delpey, M. T., F. Ardhuin, P. Otheguy, and A. Jouon (2014), Effects of waves on coastal water dispersion in a small estuarine bay, J. Geophys. Res. Oceans, 119, doi:10.1002/2013JC009466.

1. Introduction et al., 2009]. Waves also affect exchanges between the nearshore and the inner shelf [Lentz et al., 2008]. [2] Coastal waters are the receptacle for pollutants from [3] The interaction of ocean waves and nearshore cur- estuarine watersheds, especially fecal indicator bacteria rents can be decomposed in several processes. The momen- [Boehm et al., 2002; Reeves et al., 2004]. The related deg- tum carried by waves across the ocean is released in the radation of the water quality increases human health risks surf zone and captured in intense currents and sea level and leads to large economic impacts [Grant et al., 2005; changes. Waves contribute to vertical mixing in deep or Given et al., 2006]. Terrestrial storm water runoff often shallow water as turbulent kinetic energy is enhanced at the drains first onto rivers and tidal channels, finding its way surface by wave breaking [Craig and Banner, 1994; Terray into the coastal zone with freshwater inflows. In that case, et al., 1996; Feddersen, 2012a, 2012b]. The mean wave nearshore concentrations of fecal indicator bacteria are momentum, or Stokes drift [Stokes, 1847], contributes to closely related to river plumes dispersion and freshwater the advection as a surface-intensified current which adds to exchanges with the inner shelf [e.g., Ahn et al., 2005]. Estu- the mean current. Following the pioneering work of Lon- arine bays and lagoons are particularly impacted by such guet-Higgins and Stewart [1962, 1964], modeling of surf contaminations, as freshwater concentrates in these coastal zone circulations has long been based on phase-averaged systems due to their partial separation from the ocean [e.g., and depth-averaged equations, notably due to their compu- Fiandrino et al., 2003; Pereira et al., 2009]. Depending on tational efficiency. However, it appeared that the vertical the system morphology and the local wave climate, ocean shear of the mean flow can influence lateral mixing [Svend- waves may strongly impact dispersion processes. Surf zone sen and Putrevu, 1994]. Moreover, in a vertically sheared transport and mixing affect the suspended matter along- flow, depth-integrated velocities are not representative of shore distribution and nearshore retention [Boehm et al., velocities advecting a tracer with nonuniform vertical dis- 2005; Feddersen, 2007; Spydell et al., 2007, 2009; Reniers tribution. In fact, the Stokes drift always exhibits a strong vertical shear near the surface [Miche, 1944; Ardhuin et al., 2008b]. In the nearshore, this leads to large vertical 1 Centre Rivages Pro Tech, Lyonnaise des Eaux, Bidart, France. variations of the total cross-shore current. Also, laboratory 2 Laboratoire d’Oceanographie Spatiale, IFREMER, Plouzane, France. and field observations suggested that rip currents might Corresponding author: M. T. Delpey, Centre Rivages Pro Tech, Lyon- vary from depth-uniform to depth-varying outside the naise des Eaux, Technopole Izarbel, 2, allee Theodore Monod, FR-64210 breakers, with higher velocities near the surface [e.g., Haas Bidart, France. ([email protected]) and Svendsen, 2002; Reniers et al., 2009]. To capture the ©2013. American Geophysical Union. All Rights Reserved. transport of a tracer in the presence of waves, the vertical 2169-9275/14/10.1002/2013JC009466 structure of the flow may thus be needed.

1 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

[4] During the last decade, wave-current three-dimen- nearshore areas, it may be impacted by runoff pollution sional (3-D) approaches have been proposed to account for carried with river inflows. River plumes are characterized the vertical shear of wave momentum and forcing [e.g., by a remarkable stratification in the bay, with freshwater Groeneweg, 1999; Mellor, 2003; Mc Williams et al., 2004; concentrated in a thin surface layer. Ardhuin et al., 2008b; Aiki and Greatbatch, 2012]. Some [6] The present work focuses on the effect of waves on of these have been further adapted into existing ocean river plume dynamics and on water exchanges between the numerical models and applied to reproduce observed circu- bay and the inner shelf. Due to the limited field data set lations [e.g., Uchiyama et al., 2009] and nearshore disper- available in the bay for now [Delpey, 2012] and the diffi- sion [e.g., Reniers et al., 2009]. The main distinctions culty to use point measurements for the study of complex between the different formulations are (1) the use of an flows, this paper proposes an analysis based on wave- Eulerian or Lagrangian point of view and (2) the separation current numerical modeling, as a first step in the investiga- or not of the momentum into wave and mean flow contribution of the complex dynamics of the bay. An original tions [Lane et al., 2007; Bennis et al., 2011]. For the first description of main dispersion processes under the effect of aspect, truly Eulerian approach requires a mathematical wave-current interactions is provided in a realistic configu- extrapolation of the velocity profile from the trough level ration with strong 3-D features. Section 2 describes the to the mean sea level in order to define the mean flow in study site and field data. Wave and current models imple- the crest-to-trough region [Mc Williams et al., 2004]. This mentation is given in section 3. An analysis of waves trans- can be avoided in the Lagrangian framework, as the formation and modeled wave-induced circulation are then particle-following average is well defined in the whole provided in section 4, and effects of waves on freshwater water column [Andrews and McIntyre, 1978]. The second dispersion are investigated. Conclusions are summarized in difference is the distinction of wave and current momentum section 5. first introduced in depth-averaged equations by Garrett [1976]. This distinction has the main benefit of avoiding a common turbulent parameterization for both waves and 2. Study Area and Event of Interest current, as the Stokes drift is not mixed by turbulence [7] The bay of Saint Jean de Luz-Ciboure is located in unlike the mean current. It also turns out that the equation the south of the French Atlantic Coast, 10 km northward for the mean flow momentum only requires wave-induced from the Spanish border (Figure 1). This region is exposed forcing terms obtained from traditional two-dimensional to energetic swells coming mainly from North Atlantic wave models, whereas forcing for the full momentum with direction W-NW. The offshore mean significant wave requires more complex wave models, accurate to first order height and peak period are 1.6 m and 9.6 s, respectively in parameters like the bottom slope [Ardhuin et al., 2008a]. [Abadie et al., 2005]. The study site is a shallow mesotidal Taking advantages of both Lagrangian framework and bay, with tidal range about 4.5 m at spring tides. The momentum separation, Ardhuin et al. [2008b] (hereinafter bathymetry of the area is presented in Figure 1d. The bay is A08) proposed a 3-D wave-current approach based on the approximately 2 km long by 1 km wide. The area is semi- Generalized Lagrangian Mean (GLM) theory introduced enclosed by breakwaters which delimit two inlets connect- by Andrews and McIntyre [1978]. An asymptotic formula- ing the bay with the inner shelf. These shallow inlets with tion of the exact GLM-equations is provided to the second mean depth 13 and 8 m are, respectively, 250 and 350 m order in wave nonlinearities. The obtained set of equations wide. The small cross section in the inlets causes the accel- is nondivergent, thanks to a transformation of the vertical eration of tide-induced currents and related mass exchanges coordinate. The A08 formulation is consistent with Mc Wil- between the bay and the inner shelf during the tide cycle. liams et al. [2004] to the considered order of approximation Ocean waves can penetrate in the bay, especially, through in the limit of a weak mean-current vertical shear [Ardhuin the wider eastern inlet. In the northeastern part of the bay, et al., 2008b]. Bennis et al. [2011] confirmed the ability of wave breaking is regularly observed over a shallow rocky A08 formulation to provide the vertical structure of the platform. During energetic events, a high level of wave flow by numerical modeling of an adiabatic configuration. energy is dissipated in this area. The platform mean depth Michaud et al. [2012] further showed the consistency of is about 0.5 m above the Lowest Astronomical Tide (LAT) the solution obtained from A08 formulation with results level, so that a part of it is intertidal when the tidal range is from Haas and Warner [2009] and Uchiyama et al. [2010] large. The platform surface is rocky and very irregular. in the case of obliquely incident waves breaking on a plane Ponctual measurements of rock formations height show beach. Model results were further applied to a realistic con- that it often reaches several tens of centimeters high (Figure figuration on the French Mediterranean coast. 2). A steep slope connects the platform to the deeper part [5] Following these works, the A08 formulation shall be of the bay, where the bottom is mixed sandy/rocky with used in the present study. The corresponding set of equa- gentler slopes. tions was implemented in the 3-D primitive equations [8] The bay receives freshwater inflows from two small model MOHID Water [Martins et al., 2001; Braunschweig rivers (Figure 1b). The annual mean flow is 5 m3 s21 for et al., 2004]. This model is used to investigate dispersion the main river (Nivelle river) and of the order of 1 m3 s21 and mixing mechanisms in the bay of Saint Jean de Luz- for the smaller river. During intense rain events, measure- Ciboure under the combined influence of winds, tide and ments of bacterial loads (not shown) revealed that both riv- waves. The bay is a small semienclosed estuary, located in ers can receive significant inputs of fecal indicator bacteria the high-energy wave environment of the southeastern Bay in runoff from their watersheds. Such contamination pro- of Biscay (Figure 1). As a sheltered bay where the currents cess is a common feature in many coastal urban watersheds are generally weak compared to the neighboring exposed [e.g., Fiandrino et al., 2003; Reeves et al., 2004]. These

2 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

Figure 1. (a) SPOT image of the Atlantic coast on either side of the France-Spain border. SPOT4: 20 m color composite image, 22 July 2008. (b) Aerial photograph of the study site. Google Earth image, Data SIO, NOAA, U.S. Navy, 3 September 2006. (c) Photograph of the bay taken at high tide from the eastern breakwater, with the inlets on the right and the rocky platform surf zone in the center. (d) Bathymetry of the studied bay. Depth is positive downward, relative to the Lowest Astronomical Tide (LAT) level of Saint Jean de Luz harbor. Mean water level is 2.48 m above the LAT level. White squares: wave measurement locations. Red dot: Socoa tide gauge location. bacterial contaminant are then likely to be introduced into the LAT level. It recorded wave data using a sampling fre- the bay with river inflows. The following dispersion proc- quency fs 5 2 Hz. Inside the bay, two Nortek Vectors (here- esses and the related impact on water quality are an impor- inafter ADVN and ADVS) were deployed to measure tant issue for the touristic area of Saint Jean de Luz- Ciboure. [9] In this paper, the bay dynamics are examined during the episode from 22 to 28 September 2010. Environmental conditions encountered during this time interval are plotted Eastern breakwater in Figure 3. It can be seen that the studied interval corresponds to a river flood event occurring under high-energy wave conditions (max. offshore Hs 2.5 m). Wind velocity 30cm is also significant on 24 September (>10 m s21), with N to NW direction. Tidal range varies from 2.5 to 3.3 m over the time period. The bay response to the river outflow under the effect of these different forcings will be investigated. During the studied time interval, field data were collected by three bottom mounted sensors deployed in the framework of LOREA 2010 experiment (Littoral, Ocean, Rivers in Euskadi Aquitain, http://www.lorea.eu/). Sensor locations are indicated in Figure 1d. In the present work, recorded wave data will be used and compared with modeling results. A Nortek Acoustic Waves and Current profiler Figure 2. Photograph taken on the intertidal domain of (AWAC) was settled in the eastern inlet at 9 m depth under the rocky platform (northeast of the bay).

3 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

the flow model MOHID Water [Martins et al., 2001; Braunschweig et al., 2004] and the spectral wave model WAVEWATCHIIIVR (WWIII) [Tolman, 2008, 2009], using the glm2z formulation proposed by Ardhuin et al. [2008b]. [12] To predict wave-current dynamics inside the bay, the computation is carried out on three nested domains, repre- sented in Figure 4. Offshore wave conditions are first propa- gated up to the vicinity of the bay on domain G1. The domain extends approximately 30 km off the bay. The corresponding computational grid is regular with size 412 by 286 andmeshsteps100m.Wavesandcurrentarethencomputed ontwonestedlevelswithrefinedgrids(G2andG3),from approximately 20 m mean depth to the shoreline inside the bay. The second level G2 aims at providing river inflows forcing for the level G3. The flow is computed along the tidal section of both rivers up to the bay. To allow a realistic modeling of these very narrow sections with a limited grid size, a variable mesh step is adopted in G2-grid, from 100 m steps offshore to 20 m steps over the rivers upstream section. The Figure 3. (a) Mean water elevation g measured by Socoa total number of grid points is 208 by 155. The solution of tide gauge inside the bay. (b) Wind velocity Vwind and (c) level G2 is transmitted at open boundaries of the last level wind direction Dwind measured by the Socoa meteorologi- G3 (in particular flow properties at river outlets). The domain cal station (Meteo France). Hourly averages of offshore (d) G3 covers the bay area, with an offshore boundary located 1 significant wave height Hs, (e) peak period Tp (full line) km off the bay inlets. Wave computation is carried out on a and mean period Tm02 (dashed), and (f) peak direction Dp 246 by 260 regular grid with 10 m steps. Wave forcing terms (full line) and mean direction Dm (dashed). Offshore wave are then interpolated on a 123 by 130 regular grid with 20 m data were measured by the Donostia directional buoy, mesh steps for the flow computation. In levels G2 and G3, located 30 km off the bay at (22.0126 E, 43.56 N). (g) the flow model vertical discretization uses 10 sigma levels, Upstream flow of the main (full line) and the secondary with finer resolution close to the surface and at the bottom. (dashed) rivers. [13] Bathymetry of level G1 was derived from data provided by the French Navy Hydrographic and Oceanographic waves in the east part of the bay, close to the surf zone Service (SHOM). For levels G2 and G3, a compilation of (Figure 1d). The ADVN was deployed southward from the bathymetric and topographic surveys data was provided in platform, at depth 4 m, in order to provide information the framework of the LOREA project. Horizontal resolution about wave refraction and dissipation over the platform. of these data ranges from 1 m (in the deeper parts of the The ADVS was settled farther from the surf zone, also at 4 domain) to approximately 20 m (in most of the shallow areas m depth. The ADVN and ADVS recorded wave data using like the rocky platform, the intertidal domain, river sections). a sampling frequency fs 5 4 and 8 Hz, respectively. Due to a sensor dysfunction, wave data are only available from 25 3.2. Wave Model Implementation to 27 September at the ADVS location. [14] Wave transformation is simulated with the spectral [10] Some point measurements of current velocity and wave model WWIII in its version 4.04 [Tolman, 2008, salinity profile were also collected as part of LOREA 2010 2009]. WWIII has been widely validated at global and deployment. However, given the studied configuration com- regional scales [e.g., Tolman, 2002; Ardhuin et al., 2008a, plexity, the present work will not seek for an evaluation of 2010], and more recently in nearshore areas [e.g., Filipot the model ability to reproduce the few available flow measurements, but rather focus on a description of dispersion mechanisms at the scale of the whole bay, based on main G1 processes simulated by the wave-current model. A detailed 43.55 Donostia buoy Anglet description of LOREA 2010 experiment and of preliminary buoy flow model-data comparison may be found in Delpey [2012]. 43.5

43.45 3. Numerical Modeling Tide Meteo gauge station

Latitude (°) G2 3.1. General Implementation 43.4 G3 [11] The studied bay is partially exposed to energetic 43.35 wave conditions. It is also expected to involve significant Flow effects of the flow vertical structure, related to river plumes measurement dynamics in sheltered areas. To investigate freshwater dis- 43.3 −2 −1.95 −1.9 −1.85 −1.8 −1.75 −1.7 −1.65 −1.6 −1.55 −1.5 persion in this configuration, a full 3-D wave-current model Longitude (°) is used, including a representation of the vertical shear of wave momentum and forcing as well as wave-induced ver- Figure 4. Coastline (gray line), computational domains tical mixing. The present work is based on the coupling of (black dashed line), and data locations (black points).

4 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION and Ardhuin, 2012; Michaud et al., 2012; Ardhuin et al., method to discretize governing equations in a structured C- 2012]. The model solves the spectral balance equation for grid and a semi-implicit (ADI) temporal algorithm. Equa- the wave action density N, with source terms Sin, Snl, Soc, tions are numerically solved by the model with a procedure and Sbot for wind input, nonlinear four-waves interactions, equivalent to a generic vertical coordinate [Martins et al., wave breaking dissipation and bottom friction dissipation, 2001], allowing for different types of vertical discretiza- respectively. The term Soc is considered as the sum of two tion, like the sigma coordinate used for the present study. contributions Sds and Sdb, respectively, for whitecapping The numerical procedure allows a representation of the and depth-induced breaking in very shallow water. Triad wetting and drying of intertidal regions. MOHID system is interactions and bottom scattering effects are not taken into coupled to the General Ocean Turbulence Model (GOTM) account in the present study. [Burchard and Bolding, 2001] for the vertical turbulent clo- [15] The wind-wave generation and dissipation (terms sure. Detailed description of the code implementation can Sin and Sds) are parameterized according to Bidlot et al. be found in Montero [1999] and Martins et al. [2001]. The [2005]. Nonlinear four-waves interactions are modeled MOHID hydrodynamic model has been used successfully using the Discrete Interaction Approximation (DIA) as pro- in complex ocean and coastal applications [e.g., Martins posed by Hasselmann et al. [1985]. In shallow areas, like et al., 2001; Coelho et al., 2002; Leitao~ et al., 2005; Mal- the bay studied here, wave energy dissipations by bottom hadas et al., 2009] and compared well with several state- friction and depth-induced breaking become very impor- of-the-art ocean models in the Bay of Biscay [Riflet et al., tant, and Sbot and Sdb are much larger than the whitecapping 2010]. dissipation term Sds. Parameterization of the bottom friction [18] The model used in the present study, further referred dissipation term Sbot uses the linear JONSWAP formulation to as ‘‘MOHID-GLM,’’ is a new MOHID version modified [Hasselmann et al., 1973], given by to allow a full 3-D modeling of the mean flow including the effects of waves, with all other elements retained from the 2pf 2 original MOHID code. The new code version solves the S ðkÞ52C EðkÞ; (1) bot gsinh ðkDÞ glm2z asymptotic formulation of the GLM wave-current equations for the quasi-Eulerian momentum, as proposed where k is the wave number vector, f is the frequency, g is by Ardhuin et al. [2008b] and further adapted by Bennis the gravity acceleration, D is the water column height, E5 et al. [2011]. The quasi-Eulerian velocity field, noted 2pfN is the wave energy density spectrum, and C is a con- u^5ðu^1; u^2; w^ Þ, is defined as [Jenkins, 1989] stant friction coefficient. Depth-induced breaking dissipa- u^ ; u^ ; w^ 5 uL; uL; wL 2 uS ; uS; wS ; (3) tion is parameterized according to Battjes and Janssen ð 1 2 Þ ð 1 2 Þ ð 1 2 Þ [1978]. Wave heights are limited by the threshold height L L L L where u 5ðu1; u2; w Þ is the Lagrangian mean velocity Hmax 5cD, with a constant breaker parameter c. The dissi- S S S S pation term S due to depth-induced breaking is given by field and u 5ðu1; u2; w Þ is the Stokes drift velocity field. db The vertical coordinate change used by Ardhuin et al.

2 [2008b] corrects the vertical coordinate so that the glm2z Hmax Sdb ðkÞ520:25Qbfm EðkÞ; (2) equations are nondivergent. The reader is referred to Etot Appendix A for a presentation of the complete set of equations solved by MOHID-GLM, and to Delpey [2012] for a where Qb is the breaking probability ofð the random sea detailed description of the code implementation. state, fm is the mean frequency and Etot 5 EðkÞdk. For the [19] MOHID-GLM is coupled with a K2 model [Rodi, k 1980] to determine the vertical eddy viscosity and diffusiv- present application, values of parameters C and c were ity coefficients in the momentum and tracer conservation adjusted based on wave model-data comparison, as further equations. To account for the wave-enhanced vertical mix- discussed in section 4.1. ing at the surface [Agrawal et al., 1992; Terray et al., [16] Wave spectra are discretized over 25 frequencies 1996; Feddersen, 2012a, 2012b], a wave-induced surface exponentially spaced from 0.041 to 0.41 Hz so that two TKE flux is introduced in the surface boundary conditions successive frequencies fi and fi11 are related by fi1151:1fi, of the K2 scheme, and an enhanced surface roughness and 36 directions with a constant 10 directional resolution. length z0,s is used [Craig and Banner, 1994]. As proposed Offshore wave conditions are obtained from hourly direc- by Terray et al. [1996, 2000], z0,s is considered proportional spectra provided by the Donostia buoy (depth 450 tional to the total significant wave height HS, i.e., m), located 30 km off the bay at (22.0126E, 43.56N) z0;s5a0HS, with a0 a constant. Here the value a0 5 0.6, pro- (Figure 4). On the three computational levels G1 to G3, posed by Soloviev and Lukas [2003], was adopted. For the surface elevation is prescribed from the 10 min record of horizontal mixing, a constant horizontal eddy viscosity KH the Socoa tide gauge and wind forcing is given by the 2 21 was used and set to KH 5 1.0 m s (see Appendix A). hourly measurement of the Socoa meteorological station [20] The importance of bottom friction for wave-induced (see Figure 4). The current retroaction on waves is not surf zone currents has been demonstrated by several taken into account in this study. authors, especially in the longshore direction [e.g., Lon- guet-Higgins, 1970a, 1970b; Thornton and Guza, 1986]. In 3.3. Flow Model Implementation the present work, the specification of the bottom roughness [17] The present work is based on the code MOHID, a 3- length z0,b also appeared critical to the determination of D baroclinic, incompressible (Boussinesq), hydrostatic, and wave-induced currents in the surf zone. This parameter is free-surface ocean model. MOHID uses a finite volume spatialized in order to account for the variable nature of the

5 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

2 (a) 4 each river is prescribed from in situ measurements at an

(m) upstream location, where the inﬂuence of tidal oscillations Hs 1 2

AWAC on the flow is negligible (see Figure 4). The flow is then η AWAC (m) 0 0 computed along the tidal section of both rivers, which is approximately 6 km long for the main river and 3.5 km (b) long for the secondary river. At the most refined level G3, 1 open boundary conditions are imposed by the solution of Hs

ADVN (m) level G2. Both domains are forced by a homogeneous wind 0 ﬁeld, given by the hourly record of the Socoa meteorological station (Figure 4). Finally, wave related terms required (c) 1 for the ﬂow calculation are computed by WWIII from the

Hs wave ﬁeld and transmitted to MOHID-GLM every 30 min. ADVS (m) 0 4. Results 330 (d) 4.1. Wave Transformation

Dm 300

AWAC (°) 22 Observations [ ] Wave transformation inside the bay is examined 270 Model (Γ = 0.07 m2.s−3) during the time interval from 22 to 28 September. Model Model (Γ = 0.5 m2.s−3) results are compared with ﬁeld data from the Anglet buoy 330 (e) (Figure 4) and from the three bottom mounted sensors

Dm 300 deployed in the bay at this time (see section 2).

ADVN (°) [23] Figure 5 shows observed and simulated time series 270 of signiﬁcant wave height Hs and mean direction Dm at the

330 AWAC, ADVN, and ADVS locations. Measurements from (f) the AWAC allow us to identify two different wave events,

Dm 300 for which frequency spectra are plotted in Figure 6: (1) ADVS (°) 270 low-energy waves from 22 to 24 September with Hs 1m, 22 23 24 25 26 27 28 T 10 s, and D 315 and (2) a more energetic sea Day of September 2010 (UT+0h) p m state with maximum Hs 2 m and mean direction Dm Figure 5. Observed and modeled time series of hourly 325 from 24 to 28 September, which consisted in a very averaged wave height Hs at the (a) AWAC, (b) ADVN, and long swell with Tp 20 s superimposed to a shorter wave (c) ADVS location. Water level recorded by the AWAC is system with Tp 7 s. Inside the bay, a strong decrease of also plotted (gray line) in Figure 5a. Observed and modeled time series of hourly averaged mean direction Dm at the (d) 2 AWAC, (e) ADVN, and (f) ADVS location. Modeled (a) Observations results are shown for two different bottom friction coefﬁ- 2 −3 1.5 Model (Γ=0.07 m .s ) cients: the default value C 5 0.07 m2 s23 (red) and the 2 23 Model (Γ=0.5) selected value C 5 0.5 m s (blue). /Hz) 2 1

bottom in the studied site: for relatively smooth sandy Ef (m 0.5 areas, z0,b was set to 0.001 m, and for very rough rocky areas, a maximum value z 5 0.1 m was used. This latter 0,b 0 value of z0,b is large compared to more often cited values for sandy bottoms, which range usually from 0.001 to 0.01 5 m [e.g., Weir et al., 2011]. Frictional dissipation over rocky (b) seabeds has been less studied [Nunes and Pawlak, 2008]. 4 In the present conﬁguration, the value of z0,b in the rocky

/Hz) 3 area was adjusted to meet a qualitative consistency of 2 model results with preliminary flow measurements avail- 2 able in the bay (not shown). The adopted schematic param- Ef (m eterization of z0,b may be seen as a first attempt to account 1 for the unusually large roughness of the rocky platform 0 (Figure 2). However, as a tunable parameter, the selected 0 0.1 0.2 0.3 0.4 0.5 high z0,b value may also compensate for other unknown Frequency (Hz) sources of errors. As part of further work, a quantitative analysis of the roughness elements distribution over the Figure 6. Hourly averaged frequency spectra Ef at the rocky area would be required to improve the representation AWAC location from field data (black), model with the of this feature. default (red) and selected (blue) friction coefficient (a) dur- [21] For the flow computation on domain G2, surface ing the low-energy wave event (23 September at 16:00) elevations are prescribed at the offshore boundary from the and (b) during the high-energy wave event (25 September 10 min measurements of the Socoa tide gauge. The flow of at 00:00).

6 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION wave energy is observed (ADVN,S), related to important modifications of waves when propagating in the shallow eastern part of the bay. First, waves are refracted over the S-N oriented isobaths of the rocky platform. It causes wave direction to shift from incident values between 310 and 330 (AWAC) to directions ranging from 275 to 300 on the ADVN (Figures 5d and 5e). Second, wave energy is dissipated over the rocky platform, due to depth-induced breaking and bottom friction. The ADVN time series also shows that wave transformation over the platform is strongly modulated by the water level. Measured Hs at the ADVN location are approximately two times higher at high tide than at low tide. The direction shift due to refraction appears larger at low tide by 10–20 compared to high tide. [24] For the wave simulation, the breaking parameter c and the wave friction coefficient C were adjusted to (c, C) 5 (0.75, 0.5 m2 s23) on refined levels based on comparison of WWIII results with wave data recorded by the AWAC and the ADVN,S. Results obtained with selected parameters compare reasonably with field data during the 6 days interval examined here, for both low and high-energy conditions. C is essentially a tuning parameter here, cor- recting for all possible errors in the definition of the offshore boundary conditions, and necessary to produce reasonable wave parameters in the bay. The reader is referred to Appendix B for an additional discussion of this aspect and of other wave model parameters and error statistics. 4.2. Wave-Induced Circulation in the Bay [25] Wave fields computed by the WWIII model are now used to force the 3-D flow model calculation on the study area. Results of the wave-current modeling are examined during the time interval from 22 to 28 September 2010, in order to illuminate the main features of the bay circulation in response to the different nearshore forcings. Special attention is given to the effects of the increase in incident wave energy on 24 September, in order to further investigate the related impact on freshwater dynamics in the bay (next paragraphs). MOHID-GLM has been successfully validated and compared to reference wave-current models on simplified nearshore configurations [see Delpey, 2012], so that its ability to capture nearshore processes can be expected. The present work is a first step in the small-scale application of such a 3-D wave-current model to study a complex realistic circulation in a stratified environment, under both low and high-energy wave conditions. [26] Figure 7 shows the surface Lagrangian mean velocity field computed by the model at three different instants of the examined time interval: during the low-energy wave episode at low tide (Figure 7a), and during the high-energy Figure 7. Modeled surface Lagrangian mean velocity on wave episode at high tide (Figure 7b) and at low tide (Fig- 23 September 2010 at (a) 09:00 (low tide) and on 24 Sep- ure 7c). As expected in the studied mesotidal environment, tember 2010 at (b) 16:00 (high tide), and (c) 23:00 (low model results show a significant role of tide in the bay cir- tide). Velocity fields are averaged over the top 20% of the culation. In particular, the small cross section of the inlets water column. The colorscale indicates the velocity modu- and of both river mouths causes the acceleration of baro- lus. Isobaths are superimposed in gray every 1 m. tropic tidal currents, leading to mass exchanges between the rivers, the bay and the inner shelf. However, in addition direction and the orientation of the rocky platform isobaths to the tidal circulation, the wave-current modeling also sug- in the northeastern part of the bay (Figures 1 and 5), wave gests a remarkable role of waves in the circulation patterns breaking over the platform generates a longshore current inside the bay. Due to the angle between incident wave with south to southeastward direction. This feature is in

7 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

Figure 8. Fields of modeled salinity at low tide during the high-energy wave episode (26 September at 11:00) (a, b) without and (c, d) with wave forcing activated. (a, c) Average over the top 20% of the water column and (b, d) average over the lowest 20% of the water column. agreement with the relatively well known generation mech- intensity and the incident wave heights. Moreover, compar- anism first exposed by Longuet-Higgins [1970a, 1970b]. ison of Figure 7a and Figure 7c shows that for a given The intensity of the wave-induced longshore current in the water level, the location of the longshore current also surf zone is important compared to the slower circulation moves southwestward when incident wave heights in the rest of the bay. The existence of this surf zone current increase, as wave breaking occurs in the deeper western was consistent with a pilot drifter experiment performed in part of the platform, bringing another contribution to the the bay in conditions very similar to 23 September shown variability of the eastern bay circulation. in Figure 7a. An alongshore current was visually observed during the experiment with approximately the same loca- 4.3. Freshwater Dynamics tion and intensity as in the model. 4.3.1. River Plume Dispersion in the Bay [27] Surface velocity fields in Figures 7b and 7c illustrate [28] We focus on the time frame from 22 to 28 Septem- the longshore current dependence on the mean water level. ber 2010. Figure 8 gives salinity fields obtained from the 3- For a given incident wave height and direction, a decrease D wave-current model at low tide during both the high- in the mean water level results in a displacement of the energy wave episode and the river flood event. To illustrate maximum wave dissipation by breaking toward the south- the effect of waves on river plume dispersion, a model sim- western deeper part of the platform. As a consequence, the ulation is also performed without taking wave forcing into location of the induced longshore current also moves south- account. Results are given with (Figures 8c and 8d) and westward (Figure 7c). Conversely, an increase in the mean without (Figures 8a and 8b) wave forcing for both surface water level induces a displacement of the longshore current (Figures 8a and 8c) and bottom (Figures 8b and 8d) water location toward the northeastern shallower part of the plat- column layers. form (Figure 7b), which results in a strong tidal modulation [29] In both simulations, the presence of the river plumes of the wave-induced surf zone current. Figures 7a and 7c results in a thin surface layer with lower salinity and typical illustrate the correlation between the longshore current depth between 1 and 2 m. This important stratification

8 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION )

produced by the 3-D model is consistent with the few salin- −1 ity profile measurements collected in the bay (not shown, 3 15 (a) see Delpey [2012]). Salinity fields exhibit a significant 2 10 (m) s 1 5 space-time variability along the tide cycle, related to vary- H 0 0 ing river outflows and to the following freshwater disper- 5 x 10 1) Full model sion and mixing under the effect of the circulation. Wind speed (m.s 2) Model without waves 3.5 (b) [30] Comparison of model results with and without wave 3) Model without wind forcing suggests a significant effect of waves on the salinity S ) 3 4) Full model with u =0 3 field. The freshwater plume from the main river, in the east- 2.5 ern half of the bay, is particularly affected by wave-induced circulation (Figures 8a versus 8c). The surf zone longshore EFV (m 2 current over the rocky platform tends to advect salt water 1.5 into the northeastern part of the bay and thus to push fresh- 1 waters southward. It results in an accumulation of freshwater 1.5 7 (c) ) close to the main river mouth. Also, the vertical mixing over ) −1 −1 1 6 .s the rocky platform is higher with waves, due to the TKE sur- .s 3 3 face flux induced by wave breaking. It contributes to 0.5 5 increase the surface salinities in the northeastern area by 0 4 mixing the surface freshwater with the underlying ocean −0.5 3 d(EFV)/dt (m water. Without wave forcing, a larger northward and east- River flow (m ward spreading of the river plume is obtained in the surface −1 2 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 layer, with stronger stratification close to the rocky platform. Day of September (UT+0h) Moreover, comparison of Figures 8a and 8c shows that a higher freshwater outflow occurs through the bay inlets Figure 9. Time series of (a) the wave height HS measured when wave forcing is not taken into account. by the AWAC (black) and the wind speed (gray); (b) the [31] As illustrated by Figure 8, model results suggest a instantaneous (dashed) and the residual (full line) EFV; significant modification of freshwater distribution inside and (c) the time derivative of the residual EFV (colored) the bay due to the asymmetric forcing of the longshore cur- and the sum of the two river flows (gray). rent on the bay circulation. Despite its restriction to the confined and shallow surf zone area, the current induced by wave breaking is much stronger than the slower tide- and forcings, (2) a model simulation with wave forcing wind-induced circulations in the bay (especially at low switched off, (3) a wave-current simulation with wind forc- tide), so that the transport initiated in the surf zone affects ing on the flow switched off, and (4) a wave-current simu- freshwater outflow through the bay inlets. This suggests lation without Stokes drift contribution, i.e., with uS 5 0. that the wave-induced circulation could also impact fresh- The EFV time series for the four simulations are plotted in water exchanges between the bay and the inner shelf. This Figure 9, together with time series of the wind speed, the feature is now examined. incident wave height Hs and the sum of the two river flows. 4.3.2. Freshwater Balance Under the Effect of Waves In Figure 9b, the instantaneous EFV (dashed) are superim- [32] In the context of contamination processes related to posed to a residual EFV (full lines) estimated by applying a river outflows, it is interesting to examine how different 24 h 50 min average sliding window. Finally, the time forcings, here tides, winds, and waves, affect the ability of derivative of this residual EFV is plotted in Figure 9c. The the bay to evacuate freshwaters. Despite the complexity of water flux d(EFV)=dt gives the overall freshwater flow into the small-scale flow patterns inside the bay, the representa- the bay, which equals the sum of freshwater fluxes through tion of the different processes by the wave-current 3-D the two inlets and through the two river outlets. model can be used to draw tendencies in the local fresh- [34] The comparison of simulations 1 and 3 suggests that water balance in response to a rainfall event. Here the com- the wind has little effects on the freshwater balance inside puted salinity is used to establish the balance of river the bay during the examined time period, although the waters inside the bay during the time interval from 22 to 28 wind speed exceeds 10 m s21 on 24 September. On the September. As mentioned previously, this interval corre- contrary, the comparison of simulations 1 and 2 suggests a sponds to a river flood event occurring under high-energy significant effect of waves on the freshwater balance. The wave conditions (see Figure 3). The total salt quantity in computed EFV is higher in simulation 1 than in simulation the bay Qs;tot can be obtained by mixing a volume Vs of 2 at the end of the river flood event on 28 September (Fig- ocean water with salinity Ss and a volume Vf of freshwater, ure 9b). Following the increase in the river flow (on 24 so that Qs;tot 5VsSs. Introducing the total water volume in September), results of simulation 2 show a clearly corre- the bay Vtot 5Vs1Vf , an equivalent freshwater volume lated response of the bay to this freshwater input. An (EFV) can be estimated by increase of the EFV is first obtained, followed by a com- pensating decrease starting less than 16 h after the peak of Qs;tot the river flood. In simulation 1, the increase in the EFV is Vf 5Vtot 2 : (4) Ss slower but with a longer duration. The EFV decreasing phase only starts at the end of the examined time interval, [33] The EFV is computed from model results based on i.e., more than 40 h after the peak of the river flood, when four simulations: (1) a wave-current simulation with all incident wave height Hs becomes lower than 1 m. Thus,

9 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

Figure 10. Modeled surface Lagrangian mean velocity during ebb tide of day 2 for (a) (Hs, hp) 5 (0.5 m, 310 ), (b) (Hs, hp) 5 (2 m, 280 ), (c) (Hs, hp) 5 (2 m, 310 ), (d) (Hs, hp) 5 (2 m, 340 ), (e) (Hs, hp) 5 (3 m, 310 ), and (f) (Hs, hp) 5 (4 m, 310 ). Velocity fields are averaged over the top 20% of the water column. compared to simulation 2, a delay of approximately 24 h 4.3.3. Freshwater Balance Sensitivity to Incident is obtained for the EFV flux to become negative. At the Wave Characteristics and Longshore Current Velocity end of the river flood event, the EFV in simulation 1 is [36] To investigate the variability of the bay flushing about 40% higher than in simulation 2. The freshwater with incident wave characteristics, the modeled bay outflow on 27 September is of the order of 0.1 m3 s21 dynamics is now examined in a simplified configuration with waves, which is still much lower than the 0.5 m3 s21 under different offshore wave conditions. Simulations are outflow obtained without waves. performed using a sinusoidal tidal forcing of the water level [35] The obtained tendencies suggest that waves contrib- with period 12 h 25 min (corresponding to the dominant ute to maintain freshwaters inside the bay. Although the M2 component) and a constant 3 m tidal range. Wind forc- EFV increases faster without waves at the peak of the river ing is switched off and upstream river flows are constant, flood event, at the end of this event, a higher volume of set to 2.5 m3 s21 for the main river and 0 m3 s21 for the freshwater is retained inside the bay due to wave forcing. secondary river. At the offshore boundary of the domain Waves delay the evacuation of this volume and limit the G1 (Figure 4), constant wave conditions are prescribed by freshwater outflow until low-energy conditions are met. An a JONSWAP spectrum. First to investigate the effect of additional experiment performed in the wave case confirms incident wave energy, simulations are carried out using an that the extra freshwater volume retained in the bay would offshore peak period Tp 5 10 s, peak direction hp 5 310 , be subsequently evacuated from 28 to 30 September if very and significant wave height Hs in {0.5, 1, 2, 3, and 4 m}. low-energy waves were encountered during this time inter- Second to investigate the effect of incident wave direction, val (not shown). The Lagrangian transport by waves simulations are carried out with offshore Tp 5 10 s, Hs 5 2 (Stokes transport) could be a possible driving factor of m, and hp in {280 , 340 }. Finally, a simulation is also per- freshwater retention in the bay. However, a simulation with formed with wave forcing switched off. The flow model Stokes transport turned off (Figure 9, light blue lines) computation is initialized without wave forcing. Waves are shows that the Stokes drift has little contribution in the then introduced at day 0 and the subsequent bay response is present configuration. This result suggests that the outflow examined. Figure 10 shows the surface Lagrangian mean reduction is mainly due to the wave-induced longshore cur- velocity field computed by the model for different offshore rent in the eastern bay surf zone. It generates a transport wave conditions at the same time instant, during ebb tide of oriented toward the inner bay, in opposition with tidal cur- day 2. In addition, Figure 11 represents the maximum rents during ebb tide. This reduces the primary outflow of velocity Vmax of the longshore current over the simulated freshwater through the eastern inlet (also illustrated in Fig- time interval, as a function of the offshore wave height Hs. ure 8), yielding a reduction of the bay flushing during the Finally, residual EFV obtained from the ensemble of simu- examined time interval. lations are plotted in Figure 12.

10 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

1 with salinity Ss and a ﬂux Ff of freshwater, an equivalent freshwater ﬂux through the inlet cross section can be estimated from the model by 0.8

) Ss2S

−1 Ff 5Ftot : (5) 0.6 Ss

Then integrating this ﬂux over the simulated time interval, 0.4 the total freshwater volume (or EFV) exchanged through

Vmax (m.s the considered inlet is computed. The ﬂux Ff and the corre- 0.2 sponding EFV exchange are counted positively when enter- ing the bay and negatively when directed seaward. Figure 13 gives the total EFV exchange during the simulated time 0 interval partitioned into each inlet (Figure 13b) and through 0 1 2 3 4 5 Incident Hs (m) both inlets (Figure 13c, sum of EFV exchanges through both inlets). In addition, Figure 13a shows the residual

Figure 11. Maximum velocity Vmax of the wave-induced EFV in the bay at day 2. All of these freshwater volumes longshore current over the simulated time interval for the are plotted as a function of the maximum velocity Vmax of different offshore wave conditions. Black squares corre- the wave-induced longshore current over the rocky plat- spond to conditions with hp 5 310 , the black triangle and form. The value Vmax 5 0 is used to represent the no wave circle correspond to hp 5 280 and hp 5 340 , respectively. case. [40] Figure 13a shows the increase in the freshwater volume retained inside the bay for Vmax lower than approxi- 21 [37] Figure 12b shows that simulation without waves mately 0.6 m s . This corresponds to Hs < 2 m for NW (black line) gives a nearly constant residual EFV during the incident waves. In consistency with the mechanism sug- examined time interval. This results from the equilibrium gested previously, Figure 13b shows that under these wave between tidal and river inflow forcings. Considering wave conditions, the wave-induced transport initiated in the surf cases with offshore Hs 5 1 m and Hs 5 2 m (Figure 12b, zone reduces the primary freshwater outflow through the red and light blue lines), a comparable EFV increase of eastern inlet. At the same time, a larger EFV is evacuated approximately 40% is obtained at day 2, consistent with through the western inlet. However, Figure 13c suggests results from the realistic simulation exposed in the previous that this western outflow increase does not compensate the section. With offshore Hs 5 0.5 m (dark blue line), the eastern outflow reduction, as the sum of the EFV exchanges residual EFV is lower than with Hs between 1 and 2 m by through both inlets increases (reminding that it is counted approximately 15%. Figures 10a and 11 show that this EFV negatively seaward). This results in freshwater retention reduction is correlated with a reduction of the longshore inside the bay, with an increased residual EFV in the bay at current intensity Vmax, due to lower incident wave energy day 2 of the simulation. (for a given incident direction). Conversely, Figures 10e, 10f, and 11 illustrate the increase in Vmax with higher incident wave energy Hs 5 3 and 4 m compared to Hs 5 2m. 4 However, a further increase in the residual EFV with Vmax (a) is not obtained for H > 2 m. The wave-induced EFV at day 3 s (m) 2 η 2 is lower by 10% for Hs 5 3 m (Figure 12b, green line) 1 and by 25% for H 5 4 m (purple line), compared to the 5 s x 10 case with Hs 5 2m. 3.5 No waves (b) 38 Hs=0.5m,θ =310° [ ] With smaller differences, the same tendency is p Hs=1m,θ =310° obtained when examining the different incident wave direc- p Hs=2m,θ =310° tions with Hs 5 2 m. Figures 10b, 10d, and 11 show an p θ 3 Hs=3m, =310° increase in Vmax with the incident wave direction. This fea- Hs=4m,θ =310°

) p ture relates to the dependence of the longshore current 3 Hs=2m,θ =280° p Hs=2m,θ =340° velocity on the angle between incident waves and the S-N- p oriented isobaths of the rocky platform. A larger angle (i.e., EFV (m norther incoming waves) generates a stronger longshore 2.5 current. However, examining Figure 12b shows that this stronger current does not result in a higher EFV at the end of the simulation: the EFV is slightly lower for N/NW incident direction (red circles) than for NW and W/NW direc- 2 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 tion (red line and red squares). Days [39] To further investigate the relationship between Vmax and freshwater exchanges with the inner shelf, freshwater Figure 12. Time series of (a) mean water level g inside fluxes through the bay inlets are now examined. Consider- the bay and (b) residual EFV in the bay computed without ing that the total water flux Ftot through one inlet cross- (black line) and with (colored lines and symbols) wave section results from the sum of a flux Fs of ocean water forcing under different incident wave conditions.

11 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION

) vertical mixing. Although additional efforts will be 3 Residual bay (a) required for a quantitative small-scale validation of mod- m 5 eled flow patterns, the present work takes advantages of the 3 3-D model representation to propose an analysis of local dispersion processes, as a first step in the study of the com- EFV (10 2 plex bay dynamics. [44] A time interval, combining both a river flood event ) 3 10 Inlet E and an increase in incident wave energy, was examined to m 5 Inlet W (b) illustrate possible effects of waves on the bay response to 0 freshwater inputs. Results of numerical modeling suggest a −10 significant impact of waves on the bay dynamics, larger EFV (10 than wind effect during the examined time interval. −2 Obliquely incident waves refract and break over a rocky ) 3 Inlet E + W (c) platform inside the bay, resulting in a longshore current m 5 −3 strongly modulated by tide. During the examined energetic wave event (H 2 m), the computed current intensity is −4 s very large in the surf zone area, compared to the slower cir- EFV (10 −5 culation in the other deeper parts of the bay. 0 0.2 0.4 0.6 0.8 −1 [45] Modeled salinity fields show a thin surface layer Vmax (m.s ) with lower salinity, associated with river plumes spreading Figure 13. (a) Residual EFV in the bay at the end of the inside the bay. The surface layer depth and profile shape simulation (day 2), (b) total EFV exchange through the exhibit a large space-time variability along the tide cycle, eastern inlet (triangles) and through the western inlet related to transport and mixing inside the bay. During the (circles), and (c) total EFV exchange through both inlets examined high-energy wave episode, model results suggest over the simulated time interval (day 0–2), as a function of that the wave-induced longshore current reduces freshwater outflow through the bay inlets. The asymmetric wave forc- the maximum velocity Vmax of the longshore current. ing on the circulation results in a higher concentration of freshwater from the main river in the southeastern part of the bay. The model is further used to determine the related [41] On the contrary, a further increase in incident wave effects on the local freshwater balance of the bay at the energy promotes a larger bay flushing, as illustrated by Fig- scale of the river flood event. It is found that waves can ure 13a for V > 0.6 m s21. Figures 13b and 13c show max contribute to concentrate freshwater inside the bay. At the that for these larger V values, the increase in the fresh- max end of the examined event, the estimated freshwater vol- water outflow through the western inlet becomes more ume inside the bay is 40% higher and the freshwater out- important than the outflow reduction in the eastern inlet. flow is still reduced by a factor 5 due to waves. Indeed, the location of the surf zone and the very strong [46] The sensitivity of the wave-induced freshwater longshore current in the rocky area result in an even more retention to incident wave conditions was finally investi- important westward advection of freshwater masses inside gated. The analysis of model results shows a strong the bay. Freshwater finally concentrates in the western part dependence of the bay flushing to incident wave energy of the bay, close to the western bay inlet. This enables a and to the corresponding longshore current velocity. Maxi- higher freshwater outflow through the western inlet during mum freshwater volume inside the bay was found for inter- the tide cycle, which results in a reduction of the retention mediate offshore wave heights 1 m < Hs < 2 m and effect of wave forcing. 21 longshore current velocity Vmax 0.6 m s , whereas [42] Model results thus suggest a major sensitivity of the freshwater retention may be reduced by a factor 2 for lower bay flushing to the incident wave energy and the corre- 21 (Hs 0.5 m, Vmax 0.25 m s ) or higher (Hs 4m, sponding longshore current velocity. For typical incident 21 Vmax 0.8 m s ) incident wave energy. peak period Tp 5 10 s and peak direction hp 5 310 , maxi- [47] The wave-induced reduction of the bay flushing sug- mum freshwater retention in the bay is found for H s gested by this modeling study may have a large impact on between 1 and 2 m, which corresponds to V values max the exchanges between the bay and the inner shelf. In par- between 0.5 and 0.6 m s21. This corresponds also to the ticular, it may be a key mechanism in the dispersion of ter- range of wave conditions encountered during the episode restrial contaminant carried by rivers in the near shore, from 22 to 28 September 2010, examined in this paper. contributing to determine water quality inside the bay.

5. Conclusions Appendix A: MOHID-GLM Implementation

[43] A 3-D wave-current numerical model was used to [48] This appendix presents the 3-D wave-current set of investigate the effect of tides, winds, and waves on the equations implemented in MOHID-GLM. The formulation dynamics of a small estuarine bay. In the studied configura- corresponds to Ardhuin et al. [2008b] as adapted by Bennis tion, a strong salinity stratification is associated with river et al. [2011], with some specificities related to the MOHID plumes, leading to a highly 3-D behavior. To account for model and to the studied area. A synopsis of MOHID-GLM this feature, the flow model resolves the vertical structure is given below. The reader is referred to Delpey [2012] for of wave momentum and forcing, as well as wave-induced a detailed description of the code implementation.

12 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION ð cosh ð2kz12khÞ A1. Governing Equations uS5 U SSðkÞ dk if kD < 6; (A5) a a sinh 2 kD [49] The quasi-Eulerian velocity field, noted k ð ð Þ u^5ðu^1; u^2; w^ Þ, is defined as [Jenkins, 1989] S SS ua 5 Ua ðkÞexp½ 2kðz2gÞ dk if kD 6; (A6) k L L L S S S ðu^1; u^2; w^ Þ5ðu1 ; u2; w Þ2ðu1 ; u2; w Þ; (A1) SS where k5jjkjj; r is the wave intrinsic pulsation; and Ua k 5rk E k denotes the spectrum of the surface Stokes where uL5ðuL; uL; wLÞ is the Lagrangian mean velocity ð Þ a ð Þ 1 2 drift horizontal components. The vertical component of field and uS5ðuS; uS; wSÞ is the Stokes drift velocity field. 1 2 the Stokes drift wS can be computed using the nondiver- [50] The vertical coordinate change used by Ardhuin et al. [2008b] corrects the vertical coordinate for the GLM- gence of the Stokes drift velocity field by induced vertical displacement, so that u^ and uL are nondi- ð L z S vergent. The nondivergence of u is used by the model in S S @h @ua 0 0 w ðzÞ52ua ð2hÞ 2 ðz Þ dz : (A7) its vertically integrated form, from the bottom depth h to @xa 2h @xa the mean surface elevation g^, which results in the following equation for g^ : [53] Density evolution is computed from S and T through a state relationship [UNESCO, 1981]. If C denotes S or T, S the conservation of C is expressed by @g^ @ huâi1hu i 1 a 50; (A2) @ @ t xa @C @ ðu^ 1uSÞC @ ðw^ 1wS ÞC 1 a a 1 @t @xa @z where t is the time; fx ; a 2½1; 2g are the horizontal space (A8) a @ @C @ @C coordinates; z is the vertical coordinate; hð:Þi denotes 5 KH 1 KC 1SC; depth-integrated variables; and the summation convention @xa @xa @z @z for repeated indices is used. It should be noted that the vertical coordinate change used by Ardhuin et al. [2008b] cor- where KC and SC are the vertical eddy diffusivity and the rects the quasi-Eulerian free surface position z5g^ for the source term associated with the tracer C, respectively. In Stokes correction of g, so that it is equal to the local phase- equation (A8), the horizontal eddy diffusivity for C is equal averaged free surface position z5g. to the horizontal eddy viscosity, both noted KH. [51] The conservation equation implemented in A2. Boundary Conditions for the Quasi-Eulerian Flow MOHID-GLM for the quasi-Eulerian momentum is given [54] Boundary conditions in MOHID-GLM allow to in a flux-divergence form by account for different effects of waves on the quasi-Eulerian hi flow. Kinematic surface and bottom boundary conditions S S are, respectively, given by @u^ @ ðu^b1ubÞuâ @ ðw^ 1w Þu^ a 1 1 a @t @xb @z @g^ S @g^ S H J 1 uâ1ua 5w^ 1w at z5g^ðx1; x2; tÞ; (A9) 1 @p @S S @u^b (A3) @t @xa 52 2 1ub q @xb @xb @xa 0 @ @uâ @ @uâ 1 KH 1 KV ; S @ð2hÞ S @xb @xb @z @z uâ1ua 5w^ 1w at z52hðx1; x2Þ: (A10) @xa H where q0 is the water mean density; p denotes the mean pressure, which is assumed to be hydrostatic; SJ is the [55] Fluxes of momentum from wind and from wave breaking are introduced in the equations through the wave-induced pressure term; KH, KV are the horizontal and vertical eddy viscosities, respectively. This equation is dynamic surface boundary condition: equivalent to equations (12) and (13) in Bennis et al. S [2011] because u is nondivergent [Ardhuin et al., 2008b]. @uâ a aw oc KV 5s 2s 1s at z5g^ðx1; x2; tÞ; (A11) Here the momentum equation is implemented using the @z a a a Cartesian z-coordinate, as the numerical resolution is a always achieved by MOHID in the Cartesian space for any where s is the total momentum flux from the atmosphere type of vertical discretization (Cartesian or not), with a pro- to the ocean (wind stress), computed from the local wind speed using a quadratic friction law, as proposed by Large cedure equivalent to a generic vertical coordinate [see Mar- aw tins et al., 2001]. In the present study, a sigma vertical and Pond [1981]; s is the momentum flux from the discretization is used (terrain-following). atmosphere to waves (or wave-supported wind stress); and soc is the momentum flux from waves to the mean current [52] In equations (A2) and (A3), the wave related terms aw wo J S due to wave breaking. s and s are computed from spec- S and ua are given, respectively, by tral wave energy source terms Sin and Soc, respectively ð (introduced in paragraph 3.2.), according to Ardhuin et al. EðkÞ SJ 5 gk dk; (A4) [2009, 2010]. k sinh 2kD [56] At the bottom, the combined wave and current stress sb is computed according to Soulsby et al. [1995]. It results and in the following condition:

13 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION "# 3:2 @u^ jjsb jj [58] At land boundaries, a free slip condition is assumed K a 5sb 111:2 w V c;a b b with zero depth-integrated total mass flux in direction nor- @z jjsc jj1jjswjj (A12) mal to the boundary. at z52hðx ; x Þ; 1 2 A3. Turbulent Closure b [59] In equations (A3) and (A8), a constant value is used where the mean-current bottom stress sc and the wave- b for the horizontal eddy viscosity K . This simple parame- induced bottom stress sw are given, respectively, by H terization is used here as a first approximation, and the main features described in this paper were still obtained b b 1 0 0 sc 5q0CDjju^jju^ and sw5 q0Fwjju jju ; (A13) when testing different values of KH (not shown). However, 2 the refinement of this parameterization, e.g., to account for horizontal diffusion due to wave breaking in the surf zone with CD a Chezy-type bottom drag coefficient; Fw a bottom [e.g., Feddersen, 2007; Spydell et al., 2007, 2009], would friction coefficient; and u0 the wave orbital velocity. In be an interesting aspect to be investigated as part of further (A13) both u^ and u0 are evaluated at the top of the bottom work. boundary layer (which is not resolved here). The bottom [60] For the vertical turbulent closure, the MOHID sys- drag coefficient CD is given from a bottom roughness tem is coupled to the General Ocean Turbulence Model length z0,b by (GOTM) [Burchard and Bolding, 2001], a 1-D water col- 0 1 umn model proposing several turbulent closure schemes. In 2 the present study, a K2 model [Rodi, 1980] is used. The @ j A CD5 0 ; (A14) vertical eddy viscosity and diffusivity (KV, KC) are parame- log ðz 1z0;bÞ 2 2 21 2 z0;b terized as ðKV ; KCÞ5ðSV ; SCÞðq =2Þ ,whereq /2 is the TKE, is the TKE-dissipation rate, and SV, SC are where z0 is the distance from the top of the bottom bound- stability functions. The formulation proposed by Canuto 2 ary layer. In accordance with Soulsby et al. [1995], the fric- et al. [2001] is used for SV and SC. Equations for q /2 and tion coefficient Fw is evaluated by are given by 0 20:52 @ðÞq2=2 @ @ðÞq2=2 jju jj 5 K 1P 1P 2; (A18) Fw51:39 ; (A15) @t @z V @z s b rpz0;b @ @ KV @ 2 5 1 2 ðc1Ps1c3Pb2c2Þ; (A19) where rp52pfp, with fp the peak frequency. @t @z r @z q [57] At open boundaries, a mixed radiation-relaxation condition is used, transferring the methodology proposed with Ps and Pb the TKE productions by vertical shear and @ua @ua g by Marchesiello et al. [2001] to the present smaller scale buoyancy, respectively, given by Ps5 and Pb52 @q @z @z q0 application. A Flather radiation condition is applied for the @z ; r is the Schmidt number for ; and c1, c2, c3 are empir- barotropic flow [Flather, 1976]. The original formulation is ical constants, which are prescribed according to Canuto modified to account now for the linearized barotropic equi- et al. [2001] for this study. librium of the quasi-Eulerian flow, instead of the total flow. [61] Wave breaking can greatly affect vertical mixing as It results in the following condition at open boundaries: it provides an important source of TKE near the surface compared to Ps or Pb [Agrawal et al., 1992; Terray et al., g^2g^ 1996; Feddersen, 2012a, 2012b]. Effects of wave breaking rffiffiffiffi ext (A16) on vertical turbulence are taken into account through the D S S 56 huî1hu i n2 huêxt i1hu ext i n ; surface boundary conditions for (A18) and (A19), which g were adapted from Craig and Banner [1994], Craig [1996]

S S by Burchard [2001]. The surface boundary conditions for where gêxt ; uêxt ; u ext are the imposed values of g^; u^; u at q2=2 and are, respectively, given by the open boundary; n is the vector normal to the open boundary. In addition, a relaxation scheme is used for the @ðÞq2=2 baroclinic flow. If / denotes the horizontal components of KV 5Foc; (A20) @z the baroclinic velocity, the open boundary condition is 3 KV @ KV 3 3 C0 2 3 1 given by 5 C Foc1jðq =2Þ2 ; (A21) 0 2 0 2 r @z r 2 SV j ðz 1z0;sÞ @/ 1 52 ð/2/ Þ; (A17) 3 @ s ext with Foc the surface TKE flux due to wave breaking; C0 a t relax 0 constant; z the vertical distance from the surface; and z0,s a surface roughness length. In addition to these boundary where srelax is a relaxation coefficient, which is set a to low value in a nudging layer near the boundary and to a very conditions, Burchard [2001] established a parameterization large value in the rest of the domain. Baroclinic modes are of the Schmidt number r as a linear function of ðPs1PbÞ= 3 not radiated at open boundaries, following arguments pre- in order to obtain a behavior of the mixing length l5C0 2 3 21 0 sented, for example, by Blayo and Debreu [2005] and ðq =2Þ2 like l5jðz 1z0;sÞ near the surface, as prescribed Leitao~ et al. [2008]. A similar relaxation scheme is applied by Craig and Banner [1994]. In the present work, Foc is to salinity and temperature fields. specified from the wave breaking dissipation term Soc,

14 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION computed by the wave model according to Janssen et al. Table B1. Errors Between Observed and Simulated Wave Bulk [2004]. Wave breaking also envolves an enhanced value of Parameters at Anglet Buoy, AWAC, ADVN and ADVS Locations a z0,s [Craig and Banner, 1994], which is proportional to the From 22 to 28 September total significant wave height H in the present application S Model With Default C Model With Selected C [Terray et al., 1996, 2000]: Sensor Parameter RMSE, NRMSE RMSE, NRMSE z0;s5a0HS ; (A22) Anglet Buoy HS 13 cm, 7% 13 cm, 7% T02 0.6 s, 8% 0.6 s, 8% with a0 a constant. The studied bay shows areas exposed to D 3 3 incident waves and areas sheltered by breakwaters. The m AWAC HS 20 cm, 16% 16 cm, 13% main exposed area corresponds to the surf zone in the T02 1.5 s, 25% 1.3 s, 21% northeast of the bay, where the whole wave spectrum Dm 4 4 (including swell) can be affected by depth-induced break- ADVN HS 36 cm, 65% 17 cm, 31% ing. The rest of the domain is mostly sheltered by the T02 2.3 s, 37% 1.8 s, 31% breakwaters, so that the sea state generally consists in a Dm 8 8 ADVS H 19 cm, 50% 7 cm, 19% small wind sea which is generated locally. The total HS S T02 2.4 s, 34% 2.0 s, 32% should thus be representative of the wave spectrum part which is affected by breaking in both exposed (depth- Dm 7 7 induced breaking) and sheltered (whitecapping) areas. As a aError statistics at the ADVS location are given for the shorter time interval from 25 to 27 September (due to the sensor dysfunction). consequence, z0,s is considered proportional to the total HS, because it generally provides the scale of breaking waves in the studied bay. J [62] In the present work, wave related terms HS, fp, S , This range of C values also corresponds to the order of SS aw oc U , s , s , and Foc are computed by WWIII from the magnitude obtained for another Hawaiian reef area by wave field and source terms, and then transmitted to Cialone and Mckee Smith [2007], who used a coefficient 21 MOHID-GLM for the flow computation. cf 5 C/g between 0.05 and 0.12 m s . However, specific investigations would be required to confirm that the level Appendix B: Discussion of Wave Model Results of frictional wave dissipation over the studied rocky area and Parameterization can be comparable to that induced by coral reefs. This large C value may be necessary here to correct for all possible [63] To obtain a better agreement with field data, the errors in the definition of the offshore boundary conditions. friction coefficient in the bay has been significantly [64] Figures 5 and 6 show that the increase in C signifi- increased compared to more common values used over cantly improves model results, in particular inside the bay sand beds [e.g., Hasselmann et al., 1973]. Because of the at the ADVN and ADVS locations. Table B1 gives root- present site complexity involving combined refraction, mean-square errors (RMSE) between observed and mod- wave breaking and frictional dissipation, it is difficult to eled wave height Hs, mean period T02 and mean direction confirm the role of bottom friction in the observed wave Dm for both default and selected model parameterization. transformation. However, preliminary tests with a constant Normalized root-mean-square errors (NRMSE) are also Nikuradse roughness length of 10 cm give similar results. given for Hs and T02. The two error indicators are defined, This value is comparable to the 12 cm used for rock plat- respectively, as forms by Ardhuin and Roland [2013]. Such a high friction "# level could be related to the unusually rough surface of the 1=2 1 XN RMSE rocky platform (Figure 2) and of other rocky formations RMSE5 ðÞS 2O 2 ; NRMSE5 ; (B2) N i i RMS over the inner shelf offshore of the bay [Augris et al., i51 1999]. The importance of wave frictional dissipation has been emphasized by several authors in shallow areas with where ðOiÞi51::N and ðSiÞi51::N are the observed and simu- very rough bottoms, in particular coral reefs [e.g., Lowe lated values, respectively, and RMS denotes the root-mean- et al., 2005; Cialone and Mckee Smith, 2007; Filipot and square of ðOiÞi51::N . Error statistics are given for the three Cheung, 2012]. For example, based on field measurements sensors deployed in the bay and also for the Anglet wave on the reef flat of Kaneohe Bay, Hawaii, Lowe et al. [2005] buoy, located in the northeast of domain G1 at depth 50 m calculated the averaged value of the wave friction factor (Figure 4). fw 5 0.28 6 0.04, and mentioned that this value is 30 times [65] Results obtained with selected parameters compare larger than the typical value of 0.01 for flat sandy bottoms. reasonably with field data during the 6 days interval exam- According to the model of Madsen et al. [1988], fw can be ined here, for both low and high-energy conditions. Wave related to C by energy associated with the long swell is still overestimated by the model during the high-energy episode (Figure 6b), g possibly due to local nonresolved bathymetric effects out- C5fw pffiffiffi Urms ; (B1) 2 side the bay. The computed wave transformation in the east part of the bay reproduces the direction shift and wave dis- where Urms is the root-mean-square wave orbital velocity at sipation due to the rocky platform and the related tidal the bottom. For typical values of Urms between 0.1 and 0.5 modulation. The higher error level at the ADVN location ms21, this leads to C values between 0.2 and 1.0 m2 s23. could be related to the horizontal resolution of the

15 DELPEY ET AL.: EFFECTS OF WAVES ON COASTAL DISPERSION computational grid, which limits the representation of wave Blayo, E., and L. Debreu (2005), Revisiting open boundary conditions refraction over the complex bathymetry of the bay. Indeed, from the point of view of characteristic variables, Ocean Modell., 9(3), calculations carried out with a spectral refraction- 231–252. Boehm, A. B., S. B. Grant, J. H. Kim, S. L. Mowbray, C. D. McGee, C. D. diffraction model generally produced larger spatial gra- Clark, D. M. Foley, and D. E. Wellman (2002), Decadal and shorter dients (not shown), while giving the same patterns of wave period variability of surf zone water quality at Huntington Beach, Cali- heights at scales of 100 m and larger inside the bay. The fornia, Environ. Sci. Technol., 36(18), 3885–3892. use of a constant breaking parameter c may also be a limi- Boehm, A. B., D. P. Keymer, and G. G. Shellenbarger (2005), An analytical tation [e.g., Bruneau et al., 2011]. model of enterococci inactivation, grazing, and transport in the surf zone of a marine beach, Water Res., 39(15), 3565–3578. Braunschweig, F., P. C. Leitao, L. Fernandes, P. Pina, and R. J. J. Neves [66] Acknowledgments. M.T.D. acknowledges the support of a (2004), The object oriented design of the integrated water modelling sys- research grant from ANRT (CIFRE grant), and F.A. is supported by tem MOHID, in Proceedings of the XVth International Conference on IOWAGA and Field_AC projects. The present study was supported in part Computational Methods in Water Ressources, pp. 1–12, Elsevier, by the LOREA project, led by the Conseil General des Pyrenees Atlan- Oxford, U. K. tiques (http://www.lorea.eu/). LOREA 2010 field experiment was performed in collaboration with AZTI-Tecnalia (Marine Research Division), Bruneau, N., P. Bonneton, B. Castelle, and R. Pedreros (2011), Modeling rip G.E.O Transfert and CASAGEC. 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