On the Doppler distortion of the sea-wave spectra

Discussions on a form of a frequency spectrum of wind-driven sea waves just above the spectral maximum continue during the last three decades. In 1958 Phillips made a conjecture that wave breaking is the main mechanism responsible for the spectrum formation. That leads to the spectrum decay ∼ ω−5, where ω is the frequency of the waves. There is a contradiction between the numerous experimental data and this spectrum. The experiments show decay ∼ ω−4. There are two general ways of the explanation of this phenomenon. The first one (proposed by Banner (1990)) takes into account the Doppler effect due to surface circular currents generated by long waves in the Phillips model. The second approach ascends to the work by Zakharov and Filonenko (1968). It is based on four-wave interactions in the kinetic equation and gives good agreement with the experimental data. In this article the contribution to the Phillips model due to the Doppler effect was examined. We considered the cases of isotropic and strongly anisotropic spectra. Both analytical results and numerical computations give us an evidence to state that the Doppler effect cannot explain the divergence of Phillips model with experimental data. Correspondence to: A. O. Korotkevich, [email protected] 1