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DECEMBER 2012 A R DHUIN ET AL. 2101 Numerical Wave Modeling in Conditions with Strong Currents: Dissipation, Refraction, and Relative Wind 1 # # FABRICE ARDHUIN,* ARON ROLAND, FRANCK DUMAS, ANNE-CLAIRE BENNIS, @ & 11 ALEXEI SENTCHEV, PHILIPPE FORGET, JUDITH WOLF,** FRANC¸ OISE GIRARD, ## @@ PEDRO OSUNA, AND MICHEL BENOIT * Ifremer, Laboratoire d’Oce´anographie Spatiale, Plouzane´, France 1 Technological University of Darmstadt, Darmstadt, Germany # Ifremer, Laboratoire PHYSED, Plouzane´, France @ Laboratoire d’Oce´anologie et Ge´osciences (CNRS-UMR8187), Universite´ du Littoral-Coˆte d’Opale, Wimereux, France & Mediterranean Institute of Oceanography, CNRS, and Aix-Marseille University, and Sud Toulon-Var University, IRD, La Garde, France ** National Oceanographic Center, Liverpool, United Kingdom 11 Actimar SAS, Brest, France ## CICESE, Ensenada, Baja California, Mexico @@ Laboratoire Saint Venant, Chatou, France (Manuscript received 28 November 2011, in final form 9 July 2012) ABSTRACT Currents effects on waves have led to many developments in numerical wave modeling over the past two decades, from numerical choices to parameterizations. The performance of numerical models in conditions with strong currents is reviewed here, and observed strong effects of opposed currents and modulations of wave heights by tidal currents in several typical situations are interpreted. For current variations on small scales, the rapid steepening of the waves enhances wave breaking. Using different parameterizations with a dissipation rate proportional to some measure of the wave steepness to the fourth power, the results are very different, none being fully satisfactory, which points to the need for more measurements and further re- finements of parameterizations. For larger-scale current variations, the observed modifications of the sea state are mostly explained by refraction of waves over currents and relative wind effects, that is, the wind speed relevant for wave generation is the speed in the frame of reference moving with the near-surface current. It is shown that introducing currents in wave models can reduce the errors on significant wave heights by more than 30% in some macrotidal environments, such as the coast of Brittany, in France. This large impact of currents is not confined to the locations where the currents are strongest, but also downwave from strong current gradients. 1. Introduction measure of the spectral saturation (Banner et al. 2000). After several failed attempts (e.g., van Vledder and Because he observed a rapid decay of wave energy Hurdle 2002; Alves et al. 2003), parameterizations based facing an opposing current gradient, Phillips (1984) on this saturation idea (van der Westhuysen et al. 2005; concluded that the dissipation of the wave energy could Ardhuin et al. 2009) have now shown a clear advantage not be a linear function of the wave spectral density, over the linear parameterizations based on the statis- which led him to propose a statistical description of tical theory by Hasselmann (1974). Some recent work by breaking waves that could lead to a physically motivated Filipot and Ardhuin (2012) also demonstrated that a expression for wave dissipation (Phillips 1985). Only successful dissipation parameterization could be based recent evidence supported that the breaking probability explicitly on observed breaking wave statistics. could indeed be related in a nonlinear fashion to some However, at regional scales the advantage of these new parameterizations is probably related to their built- Corresponding author address: Fabrice Ardhuin, Ifremer, Cen- in decoupling of wind sea growth from abnormal swell tre de Brest, 29200 Plouzane´, France. interference (e.g., Ardhuin et al. 2007), a feature that E-mail: [email protected] was already introduced by Tolman and Chalikov (1996). DOI: 10.1175/JPO-D-11-0220.1 Ó 2012 American Meteorological Society Unauthenticated | Downloaded 10/03/21 07:30 PM UTC 2102 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42 At global scales, the good performance of the Ardhuin two other datasets that exhibit strong effects of currents et al. (2009) parameterization is largely due the intro- on waves, and for which the current field is well known. duction of a realistic nonlinear swell dissipation, which is These include the laboratory experiment by Lai et al. the most important ingredient for obtaining low errors. (1989), and macrotidal field data from the Iroise Sea Although breaking statistics are certainly nonlinear in (Ardhuin et al. 2009). Taken together, these three cases terms of spectral parameters, it is not clear that a non- illustrate different situations in which currents have a linear parameterization of the whitecapping dissipa- strong influence on waves. These are a strong local dis- tion term produces better results. sipation, the far field of a refraction area, and the modi- Given the original argument by Phillips (1984), we fications in the local generation of waves. The general found it interesting to go back to the effect of current question that we are addressing here is as follows: do gradients to look at the differences between parame- wave models today represent well the most important terizations, from the laboratory scale to the scale of the physical processes in the presence of strong currents? coastal ocean. The present study is also an occasion to This question is largely independent of the choice of evaluate the accuracy of current effects in wave models, numerical model. Because all source terms are not im- which has attracted only little attention. plemented in all models, and to simplify the present pa- Although many studies discuss the expected effect of per, the results shown here were obtained with the Wind currents on waves (e.g., Waseda et al. 2009), there are Wave Model II (Roland 2008), and WAVEWATCH III unfortunately very few validations of realistic numerical (Tolman 2009; Ardhuin et al. 2010), hereinafter abbre- modeling of waves in currents, with the notable excep- viated as WWMII and WWATCH. tion of Masson (1996) who used a specific model based on ray-tracing, without a full action balance. In fact, 2. Wave blocking and induced breaking there is a very broad literature on theoretical effects of currents, from Barber (1949) to the review by Peregrine As waves propagate against an increasingly strong (1976). There are at least as many descriptions of nu- current, their group velocity can become less than the merical model results with more or less academic tests opposing current, so that the wave energy is unable to (e.g., Holthuijsen et al. 1991; Tolman 1991b; Benoit et al. propagateupstream.Inthesecasesthewavesteepness 1996). Finally, the experimental evidence for current generally gets large enough to induce breaking. Here effects on waves is also abundant, from tidal currents we follow the assumption of (Chawla and Kirby 2002), (e.g., Vincent 1979; Ris et al. 1999; Wolf and Prandle which is largely supported by their experiments, that 1999) to large oceanic currents like the Gulf Stream wave transformation through the blocking region is (e.g., Kudryavtsev et al. 1995). Unfortunately, in many simply the result of propagation and dissipation associ- cases there is only limited quantitative information about ated with wave breaking. In that context, we investigate the current speed and spatial variation (e.g., Forget et al. the effects of existing dissipation parameterization, 1995; Ris et al. 1999) or the waves (e.g., Haus 2007). For and a possible support for the conclusions by Phillips that reason we will not report here attempts at global (1984) that dissipation should be a strongly nonlinear numerical wave modeling with currents (e.g., Rascle et al. function of the wave steepness. The potential numerical 2008), but only focus on experiments with relatively well singularity is avoided in both WWATCH and WWMII by known current fields. the use of spectral densities in the wavenumber–direction Our investigation started in 2003, with a measurement space and a variable wavenumber grid corresponding campaign in the English Channel and the evaluation of to fixed relative frequencies (Tolman and Booij 1998). four widely used numerical wave models. At that time, For the other models that were compared by Girard- the conclusion was that taking into account currents Becq et al. (2005), a particular treatment of the high improved the qualitative agreement between model and frequency had to be added (M. Benoit 2007, personal observed wave parameters, but the root-mean-square communication—taken from presentation at the 2007 errors of the model results were actually larger with the Globwave Meeting; available online at ftp://ftp.ifremer. currents (Girard-Becq et al. 2005). This was the occasion fr/ifremer/cersat/documentation/presentations/2007/ to fix some obvious problems in some of the numerical globwave_workshop/20070919_morning/Benoit.ppt). This models used. In particular the artificial effect of swell on consisted of enforcing an upper limit on the spectral level the wind sea growth, which is a common feature of the based on Hedges et al. (1985). parameterizations derived from Komen et al. (1984), was The blocking situation is investigated here using lab- found to be a problem. Taking advantage of improved oratory data by Lai et al. (1989). Because the global time wave model parameterizations and forcing fields, we now step in WWATCH must be larger than 1 s, WWM II revisit the data from that experiment, with the addition of (Roland 2008) is used here to solve the wave action Unauthenticated | Downloaded 10/03/21 07:30 PM UTC DECEMBER 2012 A R DHUIN ET AL. 2103 equation and investigate the effects of various dissipa- Csat u 5 s ds 2 2 u tion parameterizations. Soc(f , ) 2 [maxfB(f ) Brg ]F(f , ), (5) Br a. Dissipation parameterizations where Cds is a nondimensional constant, Br is a threshold It is interesting to note that all dissipation parame- for the saturation, and F(f, u) is the spectral density of terizations used here are quasi linear with a coefficient wave energy.1 The minor differences between Babanin that multiplies the frequency-directional power spec- et al.

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