A physical model for the narrowing of the directional sea wave spectra in the short gravity to gravity‐capillary range

Abstract

This paper gives the description of a theoretical model of the sea wave spectrum for short gravity to gravity‐capillary waves. It accounts for wind forcing, viscous damping, dissipation due to white capping, and nonlinear resonant three‐wave interactions, which are expected to be dominating over the four‐wave interactions near the gravity‐capillary transition. It is based upon the approach used by Janssen et al. [1998] for their physical omnidirectional spectral model of the sea surface. It is shown that by adding the momentum balance equation to the energy balance equation, the approach used by Janssen et al. to produce their omnidirectional sea wave spectral model may be generalized to obtain a two‐dimensional sea wave spectrum. The azimuthal behavior of the inferred sea wave spectrum is examined and shown to be consistent with spectral anisotropy of the sea wave spectrum observed at decimeter to centimeter wavelengths.