Phase-averaged Model Research Articles

An evaluation of the synergy between the wave and wind energy along the west Iberian nearshore

There is a growing interest in extracting marine renewable energy and contributing in this way to the green road towards a low-carbon future. From this perspective, the Iberian nearshore represents a coastal environment with very high potential. In this context, the objective of the work proposed herewith is to perform a joint evaluation of the wave and wind power along the west Iberian coastal environment. The analysis is structured in two time intervals. The first is the 20-year period (2001–2020), for which the ERA5 wind data have been considered. The second 20-year period (2026–2045) corresponds to the near future and in this case, wind data provided by the climate model RCA4 (Rossby Centre regional atmospheric model, version 4) have been processed and analysed, corresponding to the climate scenario RCP4.5. (Representative Concentration Pathway). The same two periods have been considered for the evaluation of wave power. In this case simulations with spectral phase averaged model SWAN (Simulating WAves Nearshore) have been performed. This wave modelling system was implemented for the entire North Atlantic basin and focused on the west Iberian coastal environment. Finally, the results also indicate that there is a good synergy between wind and wave power in the west Iberian nearshore. As a conclusion, the development of joint wind–wave projects along the west Iberian coastal environment represents a viable direction for the near future. Especially, the Northwestern part of the Iberian nearshore has a very good potential both in terms of wave and wind energy.

COMPARISON OF NUMERICAL AND EMPIRICAL ESTIMATES OF WAVE CONDITIONS IN THE LEE OF A DETACHED BREAKWATER

This paper presents a comparison of numerical and empirical methods routinely applied by practitioners to examine wave penetration in the lee of a breakwater, using a case study of a breakwater which is planned for Entrance Point, Broome in the northwest of Australia. Wave conditions representative of ambient and extreme conditions were determined from measured data captured directly offshore of the site, and an extreme cyclone metocean study (Baird, 2020). For ambient and extreme tropical cyclone conditions, waves are typically short crested at a peak period of between 4 seconds to 8 seconds. To examine the effectiveness of the offshore breakwater, empirical methods (Goda, 2000), a phase-averaged model (SWAN) and two phase-resolving model systems– the 2D Boussinesq wave model (MIKE21BW) and 3D non-hydrostatic model (MIKE3-Wave FM) - were applied.

Development, calibration and validation of a phase-averaged model for cross-shore sediment transport and morphodynamics on a barred beach

Simulating cross-shore sediment transport and associated sandbar migration is still a challenging task for phase-averaged coastal morphological models. Numerical studies have mostly relied on beach morphology prediction for calibration and validation, without examining in much detail the underlying hydrodynamics, sediment concentrations and transport rates. This paper reports on a new three-dimensional coastal morphodynamic model based on the hydrodynamic model of Zheng et al. (2017), combined with an advection-diffusion type suspended sediment transport model and the extended SANTOSS near-bed sediment transport formula of Van der A et al. (2013), to represent the key cross-shore transport mechanisms. The model is are calibrated based on comprehensive measurements from a large-scale laboratory experiment involving regular plunging breaking waves over an evolving sandbar, covering detailed comparisons on hydrodynamics, sediment suspension, transport rates, and bed level evolution. Separate validation using large scale wave flume experiments were also conducted to confirm the model's performance on different conditions. Good agreements are obtained between measurements and model results, which demonstrates the model's ability to reproduce cross-shore sediment transport processes under breaking waves correctly, given that the appropriate parameterizations for intra-wave processes are included. Model results also reveal the onshore near-bed transport is related to wave-induced near-bed streaming, wave skewness and asymmetry, and bed slope effects at different locations across the beach surface. Wave breaking-induced turbulence enhances the near-bed transport within the bed boundary layer which needs to be taken into account in order to achieve good model prediction skills.

A Sea Surface–Based Drag Model for Large-Eddy Simulation of Wind–Wave Interaction

Abstract Monin–Obukhov similarity theory (MOST) is a well-tested approach for specifying the fluxes when the roughness surfaces are homogeneous. For flow over waves (inhomogeneous surfaces), phase-averaged roughness length scales are often prescribed through models based on the wave characteristics and the wind speed. However, such approaches lack generalizability over different wave ages and steepnesses due to the reliance on model coefficients tuned to specific datasets. In this paper, a sea surface–based hydrodynamic drag model applicable to moving surfaces is developed to model the pressure-based surface drag felt by the wind due to the waves. The model is based on the surface gradient approach of Anderson and Meneveau applicable to stationary obstacles and extended here to the wind–wave problem. The wave drag model proposed specifies the hydrodynamic force based on the incoming momentum flux, wave phase speed, and the surface frontal area. The drag coefficient associated with the wind–wave momentum exchange is determined based on the wave steepness. The wave drag model is used to simulate turbulent airflow above a monochromatic wave train with different wave ages and wave steepnesses. The mean velocity profiles and model form stresses are validated with available laboratory-scale experimental data and show good agreement across a wide range of wave steepnesses and wave ages. The drag force is correlated with the wave surface gradient and out-of-phase with the wave height distribution by a factor of π/2 for the sinusoidal wave train considered. These results demonstrate that the current approach is sufficiently general over a wide parameter space compared to wave phase-averaged models with a minimal increase in computational cost. Significance Statement Understanding the physics of wind waves plays an important role in the context of numerous geophysical and engineering applications. A drag-based model is developed that characterizes the effect of the sea surface waves on the wind above. The model is validated with existing experimental datasets and is shown to be effective in predicting the average wind velocity and stress over waves with varied steepnesses and phase speeds. The ease of implementation and low computational cost of the model make it useful for studying turbulent atmospheric-scale flows over the sea surface important in offshore wind energy research as well as for modeling air–sea fluxes of momentum, heat, and mass.

Higher Order Phase Averaging for Highly Oscillatory Systems

We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is useful for deriving reduced models that can be solved numerically with more efficiency, since larger timesteps can be taken. Recently, Haut and Wingate (2014) introduced the idea of computing finite window numerical phase averages in parallel as the basis for a coarse propagator for a parallel-in-time algorithm. In this contribution, we provide a framework for higher order phase averages that aims to better approximate the unaveraged system whilst still filtering fast motions. Whilst the basic phase average assumes that the solution is independent of changes of phase, the higher order method expands the phase dependency in a basis which the equations are projected onto. We illustrate the properties of this method on an ODE that describes the dynamics of a swinging spring due to Lynch (2002). Although idealized, this model shows an interesting analogy to geophysical flows as it exhibits a slow dynamics that arises through the resonance between fast oscillations. On this example, we show convergence to the non-averaged (exact) solution with increasing approximation order also for finite averaging windows. At zeroth order, our method coincides with a standard phase average, but at higher order it is more accurate in the sense that solutions of the phase averaged model track the solutions of the unaveraged equations more accurately.

The near future expected wave power in the coastal environment of the Iberian Peninsula

The main target of the proposed work is to assess the expected wave energy dynamics in the coastal environment of the Iberian Peninsula. This study is motivated by the fact that the Iberian nearshore is considered among the most promising European coastal environments for wave energy extraction with experimental wave projects already operating there since many years. The near future period considered for this analysis is the 20-year time interval 2026–2045 under the Representative Concentration Pathway scenario 4.5 (RCP4.5). In parallel, in order to have a coherent degree of comparison, the results are compared with those corresponding to the recent past 20-year time interval 2001–2020. A wave modelling system based on the third-generation spectral phase averaged model SWAN (acronym from Simulating WAves Nearshore) was implemented for the entire North Atlantic basin and focused on the Iberian nearshore. Furthermore, calibrations and extensive validations of this wave prediction system have been performed. Thus, system reliability was evaluated both against buoy and satellite data and the results were found as having good accuracy. The wave energy data corresponding to the near future (2026–2045) are compared with those from the other 20-year period from the recent past (2001–2020). In this way, a comprehensive picture of the expected wave power dynamics in the coastal environment of the Iberian Peninsula is provided. The results show that there are no significant differences between the two periods considered, especially in the transition seasons (spring and autumn), both in terms of maximum values and also as regards the general patterns of the wave power fields. However, in the near future, a decrease of the resources is expected near to the coast in the summer season, compared to the values simulated for the recent past (from 12 kW/m to 9 kW/m). A contrary tendency corresponds to the winter season when for the near future we find a maximum value higher by about 14 kW/m than in the recent past.

Modeling wave attenuation by submerged flexible vegetation with XBeach phase-averaged model

Understanding and modeling wave attenuation by flexible vegetation have emerged as essential issues in coastal and ocean engineering. Given that the existing XBeach phase-averaged wave model can only simulate wave attenuation by rigid vegetation, and previous studies of wave energy dissipation by vegetation are mainly restricted to linear wave theory. This study aims to extend the XBeach phase-averaged wave model to simulate wave attenuation by both homogeneous and heterogeneous submerged flexible vegetation, and determine wave attenuation simulation deviation based on different wave theories. Hence, the existing flexible vegetation dynamic model is incorporated into the XBeach phase-averaged wave model. The reliability of the coupled model in simulating wave attenuation by both homogeneous and heterogeneous submerged flexible vegetation is revealed. Simulation results also demonstrate that the computed wave attenuation rate based on Stokes second-order wave theory is larger than that based on linear wave theory within the parameters used in this investigation. Meanwhile, wave attenuation simulation deviation between these two wave theories enlarges as the Ursell number increases within the parameters used in this investigation. This study can broaden the application of the XBeach model and lay the technical foundation for future engineering practice of nature-based coastal defence.

An efficient method to calculate depth-integrated, phase-averaged momentum balances in non-hydrostatic models

Analysis of the mean (wave-averaged) momentum balance is a common approach used to explain the physical forcing driving wave set-up and mean currents in the nearshore zone. Traditionally this approach has been applied to phase-averaged models but has more recently been applied to phase-resolving models using post-processing, whereby model output is used to calculate each of the momentum terms. While phase-resolving models have the advantage of capturing the nonlinear properties of waves propagating in the nearshore (making them advantageous to enhance understanding of nearshore processes), the post-processing calculation of the momentum terms does not guarantee that the momentum balance closes. We show that this is largely due to the difficulty (or impossibility) of being consistent with the numerical approach. If the residual is of a similar magnitude as any of the relevant momentum terms (which is common with post-processing methods as we show), the analysis is largely compromised. Here we present a new method to internally calculate and extract the depth-integrated, mean momentum terms in the phase-resolving non-hydrostatic wave-flow model SWASH in a manner that is consistent with the numerical implementation. Further, we demonstrate the utility of the new method with two existing physical model studies. By being consistent with the numerical framework, the internal method calculates the momentum terms with a much lower residual at computer precision, combined with greatly reduced calculation time and output storage requirements compared to post-processing techniques. The method developed here allows the accurate evaluation of the depth-integrated, mean momentum terms of wave-driven flows while taking advantage of the more complete representation of the wave dynamics offered by phase-resolving models. Furthermore, it provides an opportunity for advances in the understanding of nearshore processes particularly at more complex sites where wave nonlinearity and energy transfers are important.

A statistics-based model for cavitating polydisperse bubble clouds and their two-way-flow coupling

Phase-averaged bubbly flow models require statistical moments of the evolving bubble dynamics distributions. Under step forcing, these moments reach a statistical equilibrium in finite time. However, actual flows entail time-dependent pressure forcing and equilibrium is generally not reached. In such cases, the statistics of the evolving bubble population must be represented and evolved. Since phase-averaged models compute these moments point-wise, a low-cost algorithm for this evolution is of particular significance for large-scale simulations. We present a population-balance-based method for this purpose. The bubble dynamic coordinates are treated via a quadrature moment method and conditioned on the equilibrium bubble size. Statistics in the equilibrium bubble size coordinate are computed using a fixed quadrature rule and averaged over the period of bubble oscillation. Results show that two quadrature points in each of the bubble dynamic coordinates are sufficient to quantitatively reproduce key statistics. Further, averaging is shown to remove oscillatory behaviors that do not contribute to the moments. Together, this results in a method capable of tracking the bubble population statistics with significantly less computational expense than Monte Carlo approaches. The generality introduced by including statistics in the bubble dynamics coordinates is explored via acoustically excited bubble screen problems.

Refraction and Straining of Near-Inertial Waves by Barotropic Eddies

AbstractFast-moving synoptic-scale atmospheric disturbances produce large-scale near-inertial waves in the ocean mixed layer. In this paper, we analyze the distortion of such waves by smaller-scale barotropic eddies, with a focus on the evolution of the horizontal wavevector k under the effects of straining and refraction. The model is initialized with a horizontally uniform (k = 0) surface-confined near-inertial wave, which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Shear bands appear in the jet region as wave energy propagates downward and toward the anticyclone. When measured at a fixed location, both horizontal and vertical wavenumbers grow linearly with the time t elapsed since generation such that their ratio, the slope of wave bands, is time independent. Analogy with passive scalar dynamics suggests that straining should result in the exponential growth of |k|. Here instead, straining is ineffective, not only at the jet center, but also in its confluent and diffluent regions. Low modes rapidly escape below the anticyclonic core such that weakly dispersive high modes dominate in the surface layer. In the weakly dispersive limit, k = −t∇ζ(x, y, t)/2 provided that (i) the eddy vertical vorticity ζ evolves according to the barotropic quasigeostrophic equation and (ii) k = 0 initially. In steady flows, straining is ineffective because k is always perpendicular to the flow. In unsteady flows, straining modifies the vorticity gradient and hence k, and may account for significant wave–eddy energy transfers.

Assessing coastal hazard from extreme storms with a phase resolving wave model: Case study of Narragansett, RI, USA

Coastal hazard at the residential scale, resulting from the combined effects of storm surge and waves including dynamic set-up and wave runup, is assessed for the local 100-year Synthetic Design Storm (SDS) in Narragansett, RI, USA, based on high resolution (2 m) simulations with the nonlinear phase-resolving Boussinesq wave model FUNWAVE. The accuracy of wave-flow-structure interaction modeling is improved using a built-up DEM, defined by adding coastal structures to the bare-earth DEM. In addition, bathymetry and topography are modified to reflect post-storm conditions based on simulating the same storm with the morphodynamic model XBeach. Comparisons of FUNWAVE results with those of the phase-averaged model STWAVE, for the same storm conditions, show that including individual wave effects increases the inundated area by 13% and maximum water levels (TWL) across the shoreline by 11%, in average; however, in high runup areas (such as along exposed structures), the predicted maximum water levels can increase by up to 100%. FUNWAVE predicts maximum runups on the order of ∼1.5Hs (with Hs the offshore significant wave height), which is consistent with empirical formulae for steep seawalls (Van der Meer, 2002), and these occur at the most exposed structures, which historical records show have been periodically damaged by large storms. The maximum momentum forces predicted by FUNWAVE are much larger than those derived from STWAVE simulations (based on linear wave theory and assuming Rayleigh distributed waves), and also occur on the most exposed structures. The study provides a quantitative assessment of the local coastal hazard associated with the selected SDS at the scale of individual structures, and stresses the importance of accurately modeling individual wave effects, runups and associated forces in coastal hazard assessment modeling studies.

Penetration of Wind-Generated Near-Inertial Waves into a Turbulent Ocean

AbstractAn idealized storm scenario is examined in which a wind-generated inertial wave interacts with a turbulent baroclinic quasigeostrophic flow. The flow is initialized by spinning up an Eady model with a stratification profile based on observations. The storm is modeled as an initial value problem for a mixed layer confined, horizontally uniform inertial oscillation. The primordial inertial oscillation evolves according to the phase-averaged model of Young and Ben Jelloul. Waves feed back onto the flow by modifying the potential vorticity. In the first few days, refraction dominates and wave energy is attracted (repelled) by regions of negative (positive) vorticity. Wave energy is subsequently drained down into the interior ocean guided by anticyclonic vortices. This drainage halts as wave energy encounters weakening vorticity. After a week or two, wave energy accumulates at the bottom of negative vorticity features, that is, along filamentary structures at shallow depths and in larger anticyclonic vortices at greater depths. Wave feedback tends to weaken vortices and thus slows the penetration of waves into the ocean interior. This nonlinear effect, however, is weak even for vigorous storms.

Benchmarking of numerical models for wave overtopping at dikes with shallow mildly sloping foreshores: Accuracy versus speed

Practitioners often employ diverse, though not always thoroughly validated, numerical models to directly or indirectly estimate wave overtopping (q) at sloping structures. These models, broadly classified as either phase-resolving or phase-averaged, each have strengths and limitations owing to the physical schematization of processes within them. Models which resolve the vertical flow structure or the full wave spectrum (i.e. sea-swell (SS) and infragravity (IG) waves) are considered more accurate, but more computationally demanding than those with approximations. Here, we assess the speed-accuracy trade-off of six well-known models for estimating q, under shallow foreshore conditions. The results demonstrate that: i) q is underestimated by an order of magnitude when IG waves are neglected; ii) using more computationally-demanding models does not guarantee improved accuracy; and iii) with empirical corrections to incorporate IG waves, phase-averaged models like SWAN can perform on par, if not better than, phase-resolving models but with far less computational effort.

Influence of Time and Frequency Domain Wave Forcing on the Power Estimation of a Wave Energy Converter Array

Industry-specific tools for analyzing and optimizing the design of wave energy converters (WECs) and associated power systems are essential to advancing marine renewable energy. This study aims to quantify the influence of phase information on the device power output of a virtual WEC array. We run the phase-resolving wave model FUNWAVE-TVD (Total Variation Diminishing) to generate directional waves at the PacWave South site offshore from Newport, Oregon, where future WECs are expected to be installed for testing. The two broad cases presented correspond to mean wave climates during warm months (March–August) and cold months (September–February). FUNWAVE-TVD time series of sea-surface elevation are then used in WEC-Sim, a time domain numerical model, to simulate the hydrodynamic response of each device in the array and estimate their power output. For comparison, WEC-Sim is also run with wave energy spectra calculated from the FUNWAVE-TVD simulations, which do not retain phase information, and with wave spectra computed using the phase-averaged model Simulating WAves Nearshore (SWAN). The use of spectral data in WEC-Sim requires a conversion from frequency to time domain by means of random superposition of wave components, which are not necessarily consistent because of the linear assumption implicit in this method. Thus, power response is characterized by multiple realizations of the wave climates.

Predicting the hydrodynamic response of a coastal reef-lagoon system to a tropical cyclone using phase-averaged and surfbeat-resolving wave models

Tropical Cyclone (TC) Olwyn travelled along the coast of Ningaloo Reef in northwestern Australia as a Category 3 TC during 12–13 March 2015 with sustained wind speeds of over 130 km h−1 and significant wave heights on the forereef reaching 6 m. Observations from TC Olwyn showed that, contrary to typical wave transformation patterns across a coastal reef-lagoon, under the TC conditions there was a substantial shoreward increase of wave height. This unusual pattern was primarily due to strong local wind wave generation under the extreme wind conditions, despite the lagoon itself being relatively small (order 1 km wide) and shallow (order 1 m depth). Two common types of coastal numerical wave models that include either wave growth (i.e. the phase-averaged model SWAN) or infragravity waves (i.e. the surfbeat resolving model XBeach), but not both processes, were used to assess the capabilities of numerical models to predict the cyclone-induced hydrodynamics. Model results showed that wave conditions in the lagoon and at the shoreline were dominated by locally-generated wind waves, with the reef efficiently dissipating the large incident waves offshore. The infragravity waves in the lagoon were only of secondary importance during the TC compared to the locally-generated sea-swell waves. Although both the phase-averaged (SWAN) and surfbeat-resolving (XBeach) models were able to predict some of the local hydrodynamic responses, for this specific site and storm, the use of a phase-averaged model yielded the most accurate predictions of the hydrodynamics given that it included wind wave growth. However, because the influence of infragravity waves cannot be neglected in reef environments in general, these results emphasize the need for a more general modeling approach that requires the addition of wind wave growth formulations into surfbeat- or fully-phase resolving classes of numerical wave models and/or the addition of an infragravity wave formulation in spectral wave models.

A quantitative comparison of phase-averaged models for bubbly, cavitating flows

We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh–Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble- and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.

A model chain approach for coastal inundation: Application to the bay of Alghero

Coastal inundation is an important threat for many nearshore regions worldwide, and has significantly increased in the last years also due to sea-level rise and augmented impact of extreme events, like sea storms. Many countries and regions have recently invested to overcome such problems, which commonly lead to structure damages, beach erosion and many other consequences. Numerical modeling is an important tool for coastal inundation prediction, being a valuable support for management issues to mitigate the inundation risk or suggest resilient solutions. The present work illustrates a novel approach, based on a numerical model chain that exploits a tide-surge-wave operational modeling system (Kassandra), a phase-averaged model (ROMS-SWAN) for the wave propagation towards the shore, and a phase-resolving solver (NSWE) for the prediction of runup and coastal inundation. Such a chain is applied to the bay of Alghero (Sardinia, Italy), where the results of the mentioned chain are compared to those obtained using, in place of the phase-averaged model, an analytical model for the wave propagation. Results confirm that both chain approaches provide comparable inundations, though the use of the analytical, more approximate (e.g., less accurate and reliable description of wave breaking dissipation), model suggests more severe conditions and larger flooded areas. Our contribution provides a methodological approach for an accurate and reliable estimate of coastal flooding.

INDIVIDUAL WAVE EFFECTS ON COASTAL STRUCTURE DAMAGE DURING WINDSTORMS

In hazard assessment studies that evaluate the damage caused to coastal structures by windstorm-generated surge and waves, the standard approach has been to estimate structural loading by applying phase-averaged wave propagation models (e.g., SWAN, STWAVE) and storm surge models (e.g., ADCIRC), coupled or not with each other. Bare-earth “Digital Elevation Models” (DEMs) have typically been used as a basis for model grid development, with sometimes empirical adjustments being made to beach profiles or dune crest levels to account for storm-induced erosion. In recent work, the latter approach has been improved by including real time morphodynamic changes in simulations, using models such as XBeach (e.g., Schambach 2017; Schambach et al., 2017), which are still based on the wave action conservation equation, including semi-empirical parameterizations of wave breaking and many formulations based on linear wave theory (e.g., phase/group velocity, radiation stresses,…), as well as low-order wave-wave interaction terms. Finally, structural damage has typically been estimated based on empirical damage curves, developed based on field surveys, that use flow depth and controlling wave crest height as inputs (e.g., Grilli et al., 2017). Neglected in this modeling approach, however, are dynamic set-up and runup effects, as well as strongly nonlinear wave interactions that occur near and in the surf and swash zones.

Evaluation of the new coastal protection scheme at Mamaia Bay in the nearshore of the Black Sea

The target area of the proposed study, Mamaia beach, is a narrow stretch of sand barrier island that sits between the Siutghiol Lake and the Black Sea. In the northern part of the bay, is located the Midia Port, where between 1966 and 1971 a long extension of 5 km of the offshore was built. Because of this extension, the natural flow of sediments has been significantly changed. Thus, the southern part of the Mamaia Bay had less sand nourishment which meant that the coast was eroding and to prevent it a protection of six dikes was built. After approximately forty years of coastal erosion, the south of the Mamaia Bay had in 2016 a new protection scheme, which includes first of all the beach nourishment and a new dike structure (groins scheme for protection) to protect it. From this perspective, the objective of the proposed study is to evaluate the effectiveness of the old Master plan against the new one by modeling the outcome of the two scenarios and to perform a comparison with a third one, in which the protection dikes do not exist and only the artificial nourishment has been done. In order to assess the wave processes and the current patterns along the shoreline, a complex computational framework has been applied in the target area. This joins the SWAN spectral phase averaged model with the 1D surf model. Furthermore, new UAV technology was also used to map out, chart and validate the numerical model outputs within the target zone for a better evaluation of the trends expected in the shoreline dynamics.

Modeling wave attenuation induced by the vertical density variations of vegetation

A phase-averaged model, SWAN, and a phase-resolving RANS-type numerical model, NHWAVE, were compared to previously reported physical model data to evaluate the effectiveness of these models in simulating the attenuation of irregular waves propagating over emergent vegetation with variations in stem heights. The physical model was conducted with two treatments of vegetation, one with a uniform stem height and the other with different heights approximating a linear distribution in stem density over the vertical. The number of stems in the second treatment was doubled so that the total projected area over the vertical was the same between the two tests. The drag coefficients CD used by SWAN-SL (single-layer in SWAN), SWAN-ML (multi-layer in SWAN) and NHWAVE to model the presence of the vegetation were calibrated separately against the physical model data after removing the effects of bottom and sidewall friction. Although it was expected that every model would have to be recalibrated for a given wave condition and water depth due to the dependence of CD on the Keulegan–Carpenter number, this paper showed that it was also necessary to recalibrate CD in SWAN-SL for a given wave condition and water depth when the two different vegetation treatments were applied. Conversely, it was shown that the CD values in NHWAVE and SWAN-ML changed very little between the two treatments, highlighting the utility of a layered SWAN and RANS model for estimating wave attenuation when the aboveground biomass is no longer uniform over the vertical. The vertical structure of vegetation-induced turbulent kinetic energy, eddy viscosity and dissipation rate were investigated numerically using NHWAVE.