A New Model for Nonlinear Wind Waves. Part 2. Theoretical Model

Abstract

A first‐order theory for the development of a wind‐driven wave field is proposed. This takes advantage of the physical interpretation presented by Lake and Yuen (1978) that a nonlinear wind‐wave system can be completely characterized, to first approximation, by a single nonlinear wave train with carrier frequency coinciding with the local dominant frequency. The result is the nonlinear Schrodinger equation for the wave envelope, supplemented by an equation describing the change of dominant‐wave frequency (or wavenumber) with fetch (or duration). The latter equation is a consequence of a form‐drag model proposed by Deardorff (1967) for the input of wind energy into the dominant wave. The extension of the model to a random wave field is briefly discussed.