High‐Wave‐Number/Frequency Attenuation of Wind‐Wave Spectra

Abstract

Properties of surface‐elevation spectra representative of nonlinear deep‐water wind waves are examined theoretically. For a wave field characterized by second‐order nonlinearities, expressions describing the spatial covariance and the directional wave‐number spectrum of the surface geometry are derived. The nature of these quantities are then examined with emphasis on the high‐wave‐number attenuation of spectral amplitudes. It is found that, if the spectrum of the firstorder linear wave field decays as