Wave-averaged Model Research Articles

Predicting coastal impacts by wave farms: A comparison of wave-averaged and wave-resolving models

Wave energy converters (WECs) will have to be arranged into arrays of many devices to extract commercially viable amounts of energy. To understand the potential coastal impacts of WEC arrays, most research to date has relied on wave-averaged models given their computational efficiency. However, it is unknown how accurate wave-averaged model predictions are given a lack of validation data and their inherent simplifications of various hydrodynamic processes (e.g., diffraction). This paper compares the predictions of coastal wave farm impacts from a coupled wave-averaged and flow model (Delft3D-SNL-SWAN), to a wave-resolving wave-flow model (SWASH) that intrinsically accounts for more of the relevant physics. Model predictions were compared using an idealized coastal bathymetry over a range of wave conditions and wave farm geometries. Both models predicted the largest impacts (changes to the nearshore hydrodynamics) for large and dense wave farms located close to the shore (1 km) and the smallest impacts for the small and widely spaced farm at a greater offshore distance (3 km). However, the wave-resolving model generally predicted somewhat larger impacts (i.e., changes to the nearshore wave heights, mean velocities and mean water levels). We also found that coupling the wave-averaged model to a flow model resulted in more realistic downstream predictions than the stand-alone wave-averaged model.

Interaction of near-inertial waves with an anticyclonic vortex

AbstractAnticyclonic vortices focus and trap near-inertial waves so that near-inertial energy levels are elevated within the vortex core. Some aspects of this process, including the nonlinear modification of the vortex by the wave, are explained by the existence of trapped near-inertial eigenmodes. These vortex eigenmodes are easily excited by an initialwave with horizontal scale much larger than that of the vortex radius. We study this process using a wave-averaged model of near-inertial dynamics and compare its theoretical predictions with numerical solutions of the three-dimensional Boussinesq equations. In the linear approximation, the model predicts the eigenmode frequencies and spatial structures, and a near-inertial wave energy signature that is characterized by an approximately time-periodic, azimuthally invariant pattern. The wave-averaged model represents the nonlinear feedback of the waves on the vortex via a wave-induced contribution to the potential vorticity that is proportional to the Laplacian of the kinetic energy density of the waves. When this is taken into account, the modal frequency is predicted to increase linearly with the energy of the initial excitation. Both linear and nonlinear predictions agree convincingly with the Boussinesq results.

Simulating wave runup on an intermediate–reflective beach using a wave-resolving and a wave-averaged version of XBeach

The prediction of wave runup, as well as its components, time-averaged setup and the time-varying swash, is a key element of coastal storm hazard assessments, as wave runup controls the transitions between morphodynamic response types such as dune erosion and overwash, and the potential for flooding by wave overtopping. While theoretically able to simulate the dominant low-frequency swash, previous studies using the infragravity-wave–resolving model XBeach (XBSB) have shown an underestimation of the observed swash variance and wave runup, which was in part related to the absence of incident-band swash motions in the model. Here, we use an incident-band wave-resolving, non-hydrostatic version of the XBeach model (XBNH) to simulate wave runup observed during the SandyDuck '97 experiment on an intermediate–reflective sandy beach. The results show that the XBNH model describes wave runup and the individual setup and swash components well. We subsequently examine differences in wave runup prediction between the XBSB and XBNH models and find that the XBNH model is a better predictor of wave runup than XBSB for this beach, which is due to better predictions of both the incident-band and infragravity-band swash. For a range of beach states from reflective to dissipative it is shown that incident-band swash is underestimated by XBSB relative to XBNH, in particular for reflective conditions. Infragravity-band swash is shown to be lower in XBSB than XBNH for most conditions, including dissipative conditions for which the mean difference is 16% of the deep water wave height. The difference in infragravity-band swash in XBNH relative to XBSB is shown to mainly be the result of processes occurring outside the swash zone, but approximately 15% of the difference is caused by explicitly resolving incident-band wave motions within the swash zone, such as swash-swash interactions, which inherently cannot be simulated by wave-averaged models.

Wave-resolving shoreline boundary conditions for wave-averaged coastal models

Downscaling broadscale ocean model information to resolve the fine-scale swash-zone dynamics has a number of applications, such as improved resolution of coastal flood hazard drivers, modeling of sediment transport and seabed morphological evolution. A new method is presented, which enables wave-averaged models for the nearshore circulation to include short-wave induced swash zone dynamics that evolve at the wave group scale (i.e. averaged over the short waves). Such dynamics, which cannot be described, by construction through wave-averaged models, play a fundamental role in nearshore hydrodynamics and morphodynamics. The method is based on the implementation of a set of Shoreline Boundary Conditions (SBCs) in wave-averaged models. The chosen set of SBCs allows for proper computation of the short-wave properties at a mean shoreline (xl) taken as the envelope of the actual shoreline. The suitability of the approach is assessed through implementation of the SBCs into the Regional Ocean Modeling System (ROMS) coupled to a spectral wave model (InWave for IG waves and SWAN for wind waves). As the aim is to assess the viability of the approach, the SBCs are implemented only through a one-way coupling to ROMS (i.e. ROMS forcing the SBCs). Four different test cases – with constant, periodic and bichromatic offshore forcing – are run to assess the model performances. The main results of the analysis are: (a) the proposed SBCs can well reproduce the shoreline motion and swash zone dynamics in there for all chosen tests (RMSE and BIAS less than 20 % up to a cross-shore resolution of 4.0m (L0∕3 or L0∕5)) and (b) implementation of the SBCs allows ROMS to accurately simulate the swash zone flows even at a resolution 40 times coarser than that needed by ROMS with its own wet–dry routine to properly describe the same flows. The latter result clearly demonstrates the major computational advantage of using the proposed SBCs. We also show that most of the swash zone dynamics is due to the mean flow (i.e. incoming Riemann variable) and the local (at xl) wave height. However, especially in the case of bichromatic waves, the swash zone water volume content also seems to play a crucial role.

Topographically-induced enstrophy production/dissipation in coastal models

Vorticity and enstrophy production and dissipation are studied for both wave-averaged and wave-resolving (Boussinesq-type) models of wave-induced near shore circulation. Quadratic flow properties of fundamental importance for shallow-water turbulence, i.e., energy and enstrophy, whose sources/sinks are clearly identifiable by positive/negative-definite contributions in the appropriate transport equations, are taken as the most suitable indicators for assessing model performance in describing flows characterized by large-scale vortices. Two state-of-the-art models, SHORECIRC and FUNWAVE2D, have been evaluated in detail. Suitable transport equations for enstrophy are derived and analyzed to get a clear insight into the mechanisms of generation/dissipation of this quantity in both models. Analytical results show that steep gradients of the total flow depth act as sinks as well as sources for vorticity and entrophy, similar to the results of Brocchini and Colombini [M. Brocchini and M. Colombini, Phys. Fluids 16, 2469 (2004)]. Predictive estimates have been given for the rate of change of circulation for waves breaking over a bar or breakwater and the vorticity source and sink terms have been numerically analyzed. The comparison between numerical results obtained using the two different circulation models reveals that while wave-resolving computations give well-structured rip currents, the wave-averaged model predicts less organized flows, given the different structure of the circulation forcing terms. The analysis of equivalent enstrophy-forcing terms characterizing the two models shows that they are all proportional to depth gradients in the case of wave-resolving models while their intensity is mainly due to the gradients of the wave-induced velocity for wave-averaged models. Energetic considerations are also given in support of the proposed vorticity/enstrophy generation mechanisms. Wave-averaged computations clearly show that, apart from bottom friction, the most intense dissipation mechanism is due to classic viscous effects [−νT(∇ω̃)2] while depth gradients weakly contribute. Rather surprisingly this also occurs for the wave-resolving model.

Integral flow properties of the swash zone and averaging. Part 2. Shoreline boundary conditions for wave-averaged models

Shoreline boundary conditions for nearshore hydrodynamic models are discussed on the basis of the swash zone equations of Brocchini & Peregrine (1996). Swash zone flows are investigated further using the shallow water equations. Results from numerical computations are used to guide approximation to provide more practical boundary conditions for wave-averaged flows. Approximate boundary conditions, valid for small values of the rate of change of the mean water volume in the swash zone, are found which allow explicit computation of a non-zero mean water depth at the mean shoreline. This is computed in terms of the local height of the short waves. Implementation issues are also discussed.

Vertical variation of the flow across the surf zone

This paper reviews recent advances that have been made in the numerical modelling and measurement techniques of the surf zone. The review is restricted by the assumption of a long and uniform coastline case. Therefore, the frame of reference is the 2DV case, but including tree-dimensional processes important for this topic. During the last two decades, new measurement techniques have become available (e.g. Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV)), which have successfully been applied in numerous laboratory experiments. These methods have enabled detailed measurements of, for instance, the production, transport and dissipation of turbulence and have made a valuable contribution to our understanding of the processes in the surf zone. The first models that were developed were primarily based on assumptions directly derived from such observations. Since the development of the first numerical models in the mid-eighties, much research effort has been put into trying to improve these wave-averaged models because they can be applied at relatively low computational cost. The improved understanding of the surf-zone processes has also led to the development of more advanced intrawave models such as the Boussinesq-based models as well as the use of Navier–Stokes solvers. These new modelling techniques give a detailed description of the processes in the surf zone.

Integral flow properties of the swash zone and averaging

The swash zone is that part of a beach over which the instantaneous shoreline moves back and forth as waves meet the shore. This zone is discussed using the nonlinear shallow water equations which are appropriate for gently sloping beaches. A weakly three-dimensional extension of the two-dimensional solution by Carrier & Greenspan (1958) of the shallow water equations for a wave reflecting on an inclined plane beach is developed and used to illustrate the ideas. Thereafter attention is given to integrated and averaged quantities. The mean shoreline might be defined in several ways, but for modelling purposes we find the lower boundary of the swash zone to be more useful. A set of equations obtained by integrating across the swash zone is investigated as a model for use as an alternative boundary condition for wave-resolving studies. Comparison with sample numerical computations illustrates that they are effective in modelling the dynamics of the swash zone and that a reasonable representation of swash zone flows may be obtained from the integrated variables. The longshore flow of water in the swash zone is in many ways similar to the Stokes’ drift of propagating water waves. Further averaging is made over short waves to obtain results suitable as boundary conditions for longer period motions including the effect of incident short waves. In order to clearly present the work a few simplifications are made. The main result is that in addition to the kinematic type of boundary condition that occurs on a simple, e.g. rigid, boundary two further conditions are found in order that both the changing position of the swash zone boundary and the longshore flow in the swash zone may be determined. Models of the short waves both outside and inside the swash zone are needed to complete a full wave-averaged model; only brief indication is given of such modelling.