A third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated. The model is based on a Eulerian formulation of the discrete spectral balance of action density that accounts for refractive propagation over arbitrary bathymetry and current fields. It is driven by boundary conditions and local winds. As in other third-generation wave models, the processes of wind generation, whitecapping, quadruplet wave-wave interactions, and bottom dissipation are represented explicitly. In SWAN, triad wave-wave interactions and depth-induced wave breaking are added. In contrast to other third-generation wave models, the numerical propagation scheme is implicit, which implies that the computations are more economic in shallow water. The model results agree well with analytical solutions, laboratory observations, and (generalized) field observations.

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A third-generation wave model for coastal regions: 1. Model description and validation

A third-generation spectral wave model (Simulating Waves Nearshore (SWAN)) for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases. These verification cases represent an increasing complexity in two- dimensional bathymetry and added presence of currents. In the most complex of these cases, the waves propagate through a tidal gap between two barrier islands into a bathymetry of channels and shoals with tidal currents where the waves are regenerated by a local wind. The wave fields were highly variable with up to 3 orders of magnitude difference in energy scale in individual cases. The model accounts for shoaling, refraction, generation by wind, whitecapping, triad and quadruplet wave-wave interactions, and bottom and depth-induced wave breaking. The effect of alternative formulations of these processes is shown. In all cases a relatively large number of wave observations is available, including observations of wave directions. The average rms error in the computed significant wave height and mean wave period is 0.30 m and 0.7 s, respectively, which is 10% of the incident values for both.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JC900123

A third‐generation wave model for coastal regions: 2. Verification

1. Introduction 2. Observation techniques 3. Description of ocean waves 4. Statistics 5. Linear wave theory (oceanic waters) 6. Waves in oceanic waters 7. Linear wave theory (coastal waters) 8. Waves in coastal waters 9. The SWAN wave model Appendices References Index.

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Waves in Oceanic and Coastal Waters

Morphodynamics of Holocene salt marshes: a review sketch from the Atlantic and Southern North Sea coasts of Europe

A new, closed nonlinear integral transformation relation is derived describing the mapping of a two-dimensional ocean wave spectrum into a synthetic aperture radar (SAR) image spectrum. The general integral relation is expanded in a power series with respect to orders of nonlinearity and velocity bunching. The individual terms of the series can be readily computed using fast Fourier transforms. The convergence of the series is rapid. The series expansion is also useful in identifying the different contributions to the net imaging process, consisting of the real aperture radar (RAR) cross-section modulation, the nonlinear motion (velocity bunching) effects, and their various interaction products. The lowest term of the expansion with respect to nonlinearity order yields a simple quasi-linear approximate mapping relation consisting of the standard linear SAR modulation expression multiplied by an additional nonlinear Gaussian azimuthal cutoff factor. The cutoff scale is given by the rms azimuthal (velocity bunching) displacement. The same cutoff factor applies to all terms of the power series expansion. The nonlinear mapping relation is inverted using a standard first-guess wave spectrum as regularization term. This is needed to overcome the basic 180° mapping ambiguity and the loss of information beyond the azimuthal cutoff. The inversion is solved numerically using an iteration technique based on the successive application of the explicit solution for the quasi-linear mapping approximation, with interposed corrections invoking the full nonlinear mapping expression. A straightforward application of this technique, however, generally yields unrealistic discontinuities of the best fit wave spectrum in the transition region separating the low azimuthal wave number domain, in which useful SAR information is available and the wave spectrum is modified, from the high azimuthal wave number region beyond the azimuthal cutoff, where the first-guess wave spectrum is retained. This difficulty is overcome by applying a two-step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first-guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine-scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions.

https://pure.mpg.de/pubman/item/item_3320035_3/component/file_3320036/91JC00302.pdf

On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion

Based on the linearized form of the boundary layer equations and a simple eddy viscosity formulation of shear stress, the turbulent bottom boundary layer flow is obtained for a wave motion specified by its directional spectrum. Closure is obtained by requiring the solution to reduce, in the limit, to that of a simple harmonic wave. The resulting dissipation is obtained in spectral form with a single friction factor determined from knowledge of the bottom roughness and an equivalent monochromatic wave having the same root-mean-square near-bottom orbital velocity and excursion amplitude as the specified wave spectrum. The total spectral dissipation rate is obtained by integration and compared with the average dissipation obtained from a model considering the statistics of individual waves defined by their maximum orbital velocity and zero-crossing period. The agreement between the two different evaluations of total spectral dissipation supports the validity of the spectral dissipation model.

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Spectral wave attenuation by bottom friction: theory

The effect of wind waves on the steady wind-driven circulation in a narrow, shallow bay is investigated with a two-dimensional (y, z) circulation model and the Grant and Madsen [1979] bottom-boundary layer model, which includes wave-current interaction. A constant wind stress is applied in the along-channel x direction to a channel with a constant cross-sectional profile h(y). The wind-induced flushing of shallow bays is shown to be sensitive to both the shape of the cross section and the effects of surface waves. The flushing increases with increasing h′/h–, where h′ is the standard deviation of cross-channel depth and h– is the mean depth. This is consistent with the findings of Hearn et al. [1987]. The flushing decreases, however, with the inclusion of surface wave effects which act to increase the bottom drag felt by the currents. Increasing effective bottom friction reduces the strength of the circulation, while the along-bay surface slope, bottom stress and the structure of current profiles remain nearly unchanged. An implication of the circulation dependence on wave-current interaction is that low-frequency oscillatory winds may drive a mean circulation when the wave field changes with wind direction.

Effect of wave‐current interaction on wind‐driven circulation in narrow, shallow embayments

The third-generation wave model, WAM, is presently used to investigate the mutual consistency of the Seasat global data sets of scatterometer winds and altimeter wave heights for the complete Seasat period. While modeled and observed wave heights are in reasonable agreement on the global average, regional differences can be great and on occasion exceed 40 percent. These errors are primarily attributable to forcing wind field deficiencies; the friction velocities of the Goddard Laboratory for Atmospheres are found to be significantly underestimated in the high-wind belt of the Southern Hemisphere. A wave data assimilation scheme is presented in which the wave field is updated without change to the forcing wind field.

/pdf/validation-and-assimilation-of-seasat-altimeter-wave-heights-ou6uxv2cvd.pdf

Validation and assimilation of Seasat altimeter wave heights using the WAM wave model

Surface winds derived from atmospheric pressure fields are used as input to a finite-depth wind-wave model to predict the sea state during a cold air frontal passage over the Yellow and East China Seas, which occurred 15–18 November 1983. The predicted maximum wave-stress field near the bottom is used to examine the concept of turbulent wave intensities causing sediment resuspension. The temporal variability of the wave field at three sites is used to illustrate the dependence of the bottom response on depth within the Yellow Sea. Maps of the temporal and spatial distribution of index for initiation of sediment movement are computed for different noncohesive sediment materials during this storm period and compared to sedimentological results for this region. This study demonstrates that wave action is a mechanism which can significantly influence the sediment transport pattern induced by the regional circulation existing in this marginal sea. The results also identify regions where winter storm-g...

Storm-Generated Surface Waves and Sediment Resuspension in the East China and Yellow Seas

A parametric windsea model for arbitrary water depths is presented. The model is derived from a conservation of energy flux formulation and includes shoaling, refraction, dissipation by bottom friction, as well as finite-depth modifications of the atmospheric input and nonlinear wave–wave interaction source terms. The importance of dissipation due to a rough ocean floor on the migration of the spectral peak frequency is discussed and compared with that caused by nonlinear energy transfer. Numerical simulations are used to systematically examine wave growth and the development of the spectral peak in a depth-limited ocean. Two idealized situations of wave growth and propagation are considered to further understand the influence of bottom friction on the spectral dynamics. The first case studies the characteristics of fetch-limited wave growth in a steady, uniform wind as function of depth and bottom roughness. The second case examines the role of bottom dissipation on a fully developed deep-water ...

Hans C. Graber

Papers

Spectral wave attenuation by bottom friction: theory

Effect of wave‐current interaction on wind‐driven circulation in narrow, shallow embayments

Validation and assimilation of Seasat altimeter wave heights using the WAM wave model

Storm-Generated Surface Waves and Sediment Resuspension in the East China and Yellow Seas

A Finite-Depth Wind-Wave Model. Part I: Model Description