Wave Shape Evolution from a Phase-Averaged Spectral Model

Abstract

In spectral wave models, the nonlinear triad source term accounts for the transfer of energy to the bound higher harmonics. This paper presents an extension to commonly used spectral models that resolves the evolution of the bound wave energy by keeping track of the energy that has been bound by the triad interactions. This extension is referred to as the bound wave evolution (BWE) model. From this, the spatial evolution of the bound wave height is obtained, which serves as a proxy for the nonlinear wave shape. The accuracy of these bound wave heights, and thus wave shape predictions, is highly dependent on the accuracy of the triad source term. Therefore, in this study, the capability of the LTA and SPB triad formulations to capture the growth of the bound wave height is evaluated. For both of these formulations, it is found that slope dependent calibration parameters are required. Overall, despite being computationally more expensive, the SPB method proves to be significantly more accurate in predicting the bound wave evolution. In the shoaling zone, where the bound wave energy is dominated by triads, the BWE model is well capable of predicting the nonlinear wave’s shape. In the surf zone, however, where a combination of triads and wave breaking control the spectral evolution, the BWE model over-predicts the bound wave height. Nevertheless, this paper shows the promising capabilities of spectral models to predict the nonlinear wave shape.

Keywords

• wave shape
• bound wave height
• triads
• SWAN
• SWASH