Enhanced formulation of wind energy input into waves in developing sea

Abstract

Formulation of the wind energy input into waves in developing sea is a very important but rather difficult problem in physical oceanography. The complex flow condition within the air-sea boundary layer including wave breaking is known to be the most important factor governing the wind energy input. However, the existing theoretical and empirical models are not always satisfactory or of limited generality in taking this factor into consideration with a sufficient accuracy. In this study, a numerical method based on the conservation law for wave energy is first established to obtain the spectrum of wind energy input under different fetches. To achieve reliable results, a modified JONSWAP spectrum, which is valid not only for waves at a younger age but also for a fully-developed sea, is adopted; an accurate solution technique is employed to evaluate the nonlinear wave-wave interaction; and a significantly improved wave dissipation model, which takes into account both the inherent and the cumulative dissipation, is also suggested. An enhanced empirical formula for wind energy input into waves in developing sea is also proposed in this study. The formula takes into account the recently identified role of wave breaking and air-flow separation, i.e., the wind energy input is significantly increased if wave breaks but it is substantially reduced if air-flow separation occurs on the leeside of wave crests. It is demonstrated that the formula proposed in this study is advantageous. Both of its spectral shape and peak values are in good agreement with the numerical results based on conservation of wave energy, at either a younger or an older wave age.