|Spectral modelling of wind waves in coastal areas|
Ris, R.C. (1997). Spectral modelling of wind waves in coastal areas. Communications on Hydraulic and Geotechnical Engineering, 97-4. Delft University of Technology. Faculty of Civil Engineering: Delft. xi, 160 pp.
Deel van: Communications on Hydraulic and Geotechnical Engineering. Delft University of Technology. Department of Civil Engineering: Delft. ISSN 0169-6548
Water waves > Surface water waves > Wind waves
To estimate wave conditions in coastal areas numerical wave models of the phase averaged types can be used. The ones that represent the evolution of the waves on a grid (Eulerian) are superior to the ones that are based on wave rays (Lagrangian). Eulerian models have been developed and are widely used for applications in the deep ocean and for shelf seas. However, the physics for shallow water waves are not well described in these models and the computations are not economically feasible in coastal waters due to numerical requirements.
In the present study a wave model (SWAN) has been developed for the simulation and prediction of waves in a variety of near-shore, shallow water conditions with ambient currents. The SWAN model has been developed to provide an operational tool for users with fairly conventional computer capacity (desk top computers). It is based on an Eulerian formulation of the discrete spectral balance of action density that accounts for generation, propagation and dissipation of the waves in small scale but otherwise arbitrary wind fields, bathymetry and current fields. The kinematic behaviour of the waves is described with the linear theory for surface gravity waves (including the effects of currents). The processes of generation, dissipation and nonlinear wave-wave interactions are represented explicitly with state-of-the-art formulations. This makes the SWAN model a so called third-generation model.
In the SWAN model presented here, time has been removed from the action balance equation, which makes the model stationary. This is considered acceptable in view of the residence time of the waves in the relatively small coastal areas for which the model is intended. In contrast to all other third-generation wave models, the numerical propagation scheme is implicit (an iterative, forward marching, four sweep technique) which implies that for shallow water the computations in SWAN are one to two orders more economic than in the other models. An added advantage of this implicit scheme is that the model is very robust in practical coastal applications. Moreover, the implicit schemes allow a treatment of wave blocking and wave reflection against an opposing current that is consistent with the linear theory for surface gravity waves without any ad hoc assumptions. The deep water physics are taken from the WAM model (Cycle 3, the WAMDI group, 1988 and Cycle 4, Komen et al., 1994). These are supplemented with the shallow water processes of bottom friction (Hasselmann et al., 1973, Collins, 1972 and Madsen et al., 1988), a slightly adapted version of the Discrete Triad Approximation of Eldeberky and Battjes (1995) for the triad-wave interactions and the spectral version of the bore-based breaking model of Battjes and Janssen (1978), as adapted by Eldeberky and Battjes (1995) (and an adapted maximum wave height-to-depth ratio from Nelson, 1987).
To validate the implementation of wave propagation in SWAN, computational results have been compared with solutions from linear wave theory. To obtain the best agreement with laboratory and field observations, a selection between different expressions for the physical processes has been made and in addition, tunable coefficients were calibrated against the data for the different cases.
To verify the wave model computations have been carried out in one other laboratory and three field cases. The field cases represent an increasing complexity in two-dimensional bathymetry and added presence of wind and currents. These SWAN computations were carried out with those physical processes and (tunable) coefficients that were selected from the validation of the model. The results of the SWAN computations are compared with observations. The performance of the wave model in these cases has been quantified with a statistical analysis of the errors in integral wave parameters (significant wave height and mean wave period). It is found to be quite reasonable. However, the agreement between the observed and the computed wave spectra varies considerably.
The present computing time for cases without currents is typically between 30 min and 45 min on a desk-top computer (HP9000/735 work station, 125 MHz) for 100 X 100 geographic (water covered) grid points and 24 frequencies and 36 directions in the spectrum. With the expected performance of desk-top computers presently entering the market this will reduce to less than 15 to 30 min within the next few years. This means that from an operational point of view the SWAN model can be economically applied in a consulting environment.