L.H. Holthuijsen

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

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.

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

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.

A Method for the Routine Analysis of Pitch-and-Roll Buoy Wave Data

Abstract A simple, computationally efficient method is proposed as a standard procedure for the routine analysis of pitch-and-roll buoy wave data. The method yields four directional model-free parameters per frequency: the mean direction, the directional width, the skewness, and the kurtosis of the directional energy distribution. For most applications these parameters provide sufficient directional information. The estimation procedure and error characteristics of the parameter estimates are discussed and illustrated with computer simulated data. An optional interpretation of the combination of skewness and kurtosis as an indicator of uni-modality of the directional energy distribution is suggested and illustrated with field observations.

A prediction model for stationary, short-crested waves in shallow water with ambient currents

Abstract A numerical model for the hindcasting of waves in shallow-water ( hiswa ) is described and comparisons are made between observations and model results in a realistic field situation. The model is based on a Eulerian presentation of the spectral action balance of the waves rather than on the more conventional (at least in coastal engineering) Lagrangian presentation. Wave propagation is correspondingly computed on a grid rather than along rays. The model accounts for refractive propagation of short-crested waves over arbitrary bottom topography and current fields. The effects of wave growth and dissipation due to wind generation, bottom dissipation and wave breaking (in deep and shallow water) are represented as source terms in the action balance equation. The computational efficiency of the model is enhanced by two simplifications of the basic balance equation. The first one is the removal of time as an independent variable to obtain a stationary model. This is justified by the relatively short travel time of waves in coastal regions. The second simplification is the parameterization of the basic balance equation in terms of a mean frequency and a frequency-integrated action density, both as function of the spectral wave direction. The discrete spectral representation of wave directionality is thus retained. An untuned version of hiswa has been tested in a closed branch of the Rhine estuary where measurements with buoys and a wave gauge are available. In this situation, where wave breaking and short-crestedness dominate, rms-errors in the significant wave height and mean wave period are about 10 and 13% respectively of the observed values.

Phase-decoupled refraction–diffraction for spectral wave models

Abstract Conventional spectral wave models, which are used to determine wave conditions in coastal regions, can account for all relevant processes of generation, dissipation and propagation, except diffraction. To accommodate diffraction in such models, a phase-decoupled refraction–diffraction approximation is suggested. It is expressed in terms of the directional turning rate of the individual wave components in the two-dimensional wave spectrum. The approximation is based on the mild-slope equation for refraction–diffraction, omitting phase information. It does therefore not permit coherent wave fields in the computational domain (harbours with standing-wave patterns are excluded). The third-generation wave model SWAN (Simulating WAves Nearshore) was used for the numerical implementation based on a straightforward finite-difference scheme. Computational results in extreme diffraction-prone cases agree reasonably well with observations, analytical solutions and solutions of conventional refraction–diffraction models. It is shown that the agreement would improve further if singularities in the wave field (e.g., at the tips of breakwaters) could be properly accounted for. The implementation of this phase-decoupled refraction–diffraction approximation in SWAN shows that diffraction of random, short-crested waves, based on the mild-slope equation can be combined with the processes of refraction, shoaling, generation, dissipation and wave–wave interactions in spectral wave models.

THE "SWAN" WAVE MODEL FOR SHALLOW WATER

A study of alternatives including a shoreline evolution numerical modelization has been carried out in order to both diagnose the erosion problem at the beaches located between Cambrils Harbour and Pixerota delta (Tarragona, Spain) and select nourishment alternatives.

Wind and waves in extreme hurricanes

Waves breaking at the ocean surface are important to the dynamical, chemical and biological processes at the air-sea interface. The traditional view is that the white capping and aero-dynamical surface roughness increase with wind speed up to a limiting value. This view is fundamental to hurricane forecasting and climate research but it has never been verified at extreme winds. Here we show with observations that at high wind speeds white caps remain constant and at still higher wind speeds are joined, and increasingly dominated, by streaks of foam and spray. At surface wind speeds of ?40 m/s the streaks merge into a white out, the roughness begins to decrease and a high-velocity surface jet begins to develop. The roughness reduces to virtually zero by ?80 m/s wind speed, rendering the surface aero-dynamically extremely smooth in the most intense part of extreme (or major) hurricanes (wind speed > 50 m/s). A preliminary assessment shows that cross swell, dominant in large regions of hurricanes, allows the roughness under high wind conditions to increase considerably before it reduces to the same low values.

Hurricane Gustav (2008) Waves and Storm Surge: Hindcast, Synoptic Analysis, and Validation in Southern Louisiana

AbstractHurricane Gustav (2008) made landfall in southern Louisiana on 1 September 2008 with its eye never closer than 75 km to New Orleans, but its waves and storm surge threatened to flood the city. Easterly tropical-storm-strength winds impacted the region east of the Mississippi River for 12–15 h, allowing for early surge to develop up to 3.5 m there and enter the river and the city’s navigation canals. During landfall, winds shifted from easterly to southerly, resulting in late surge development and propagation over more than 70 km of marshes on the river’s west bank, over more than 40 km of Caernarvon marsh on the east bank, and into Lake Pontchartrain to the north. Wind waves with estimated significant heights of 15 m developed in the deep Gulf of Mexico but were reduced in size once they reached the continental shelf. The barrier islands further dissipated the waves, and locally generated seas existed behind these effective breaking zones.The hardening and innovative deployment of gauges since Hur...

Performance of the Unstructured-Mesh, SWAN+ADCIRC Model in Computing Hurricane Waves and Surge

Coupling wave and circulation models is vital in order to define shelf, nearshore and inland hydrodynamics during a hurricane. The intricacies of the inland floodplain domain, level of required mesh resolution and physics make these complex computations very cycle-intensive. Nonetheless, fast wall-clock times are important, especially when forecasting an incoming hurricane.We examine the performance of the unstructured-mesh, SWAN+ADCIRC wave and circulation model applied to a high-resolution, 5M-vertex, finite-element SL16 mesh of the Gulf of Mexico and Louisiana. This multi-process, multi-scale modeling system has been integrated by utilizing inter-model communication that is intra-core. The modeling system is validated through hindcasts of Hurricanes Katrina and Rita (2005), Gustav and Ike (2008) and comprehensive comparisons to wave and water level measurements throughout the region. The performance is tested on a variety of platforms, via the examination of output file requirements and management, and the establishment of wall-clock times and scalability using up to 9,216 cores. Hindcasts of waves and storm surge can be computed efficiently, by solving for as many as 2.3⋅1012 unknowns per day of simulation, in as little as 10 minutes of wall-clock time.

Propagation of ocean waves in discrete spectral wave models

Abstract In many numerical models for hindcasting or forecasting ocean waves, wave energy is propagated over large distances. In the class of discrete spectral models such propagation suffers from a disintegration of the initial wave field into many individual wave fields. This “garden sprinkler” effect is due to the treatment of finite spectral bands as individual wave components. It is shown in the present study that this effect can be avoided by including two correction terms in the commonly used energy balance equation of the waves. One of these terms accounts for longitudinal (frequency) dispersion, the other term accounts for lateral (directional) dispersion. These terms are derived from the energy balance of finite spectral bands and they are expressed in terms of the spectral band characteristics. Since their nature is that of diffusion terms, they are local operators, which is computationally convenient. However, the coefficients of these terms are not locally determined. To illustrate the effect of the proposed correction terms, the propagation of swell from a distant storm (oceanic scale) is computed with and without the proposed correction terms.