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.