Spectral modeling of wave to Boussinesq equations

Spectral modeling of wave to Boussinesq equations ~ Knowledge of the wave spectrum in the shoaling region and in the surf zone is of great importance to coastal engineering. Shallow-water waves are profoundly modified by bottom topography. Refraction, shoaling, triad interactions, and breaking are typical manifestations of this interaction. The understanding of these physical processes has been improved in recent years, and a number of attempts have been made to incorporate this knowledge in numerical wave models.

Two classes of spectral models can be distinguished, differing mainly in their formulations and the field of applications. In the first, phase-averaged, class of models the governing equations are formulated in terms of wave energy (or action) density. Their computational efficiency makes them feasible for wind wave prediction on the open sea. In the second, phase-resolving, class of models the equations are formulated in terms of wave amplitude and phase. These models are computationally demanding compared with the first class and are therefore restricted to smaller domains.

Spectral amplitude, phase-resolving models can incorporate nonlinear shallow-water effects, such as the generation of bound sub- and superharmonics and near-resonant triad interactions, for which substantial energy transfer can take place in relatively short distances, leading to significant changes in the spectral ‘shape as well as the wave profile [Madsen and Sorensen, 1993]. These nonlinear cross-spectral transfers of energy and phase modifications lead to the asymmetric and skewed profiles that are characteristic of nearly breaking and broken waves.

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