2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time

Abstract

AbstractA fully consistent 2D parametric model of wave development under spatially and/or time varying winds is developed. Derived coupled equations are written in their characteristic form to provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are developing and distributed under varying wind forcing conditions. For young waves, nonlinear interactions drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are governing the wave energy evolution. With a prescribed wind wave growth rate, proportional to (u*/c) squared, wave breaking dissipation must follow a power‐function of the dominant wave slope. For uniform wind conditions, this choice for the growth rate imposes solutions to follow fetch laws, with exponents q = −1/4, p = 3/4 correspondingly. This set of exponents recovers the Toba's laws, and imposes the wave breaking exponent equal to 3. A varying wind direction can then drive spectral peak direction changes, leading to the occurrence of focusing/defocusing wave groups over localized areas where wave‐rays merge and cross. Significant (but finite) local variations of the energy are then expected under varying wind forcing. Propagating away from a stormy area, wave rays generally diverge, leading to dispersive swell systems. Examples of practical applications of this model are provided in (Kudryavtsev et al., 2021, companion paper).