On the Doppler distortion of the sea-wave spectra

Abstract

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.

Influence of the condensate and inverse cascade on the direct cascade in wave turbulence

“…Simple mechanism of condensate interaction with short waves of direct cascade was proposed. This interaction along with other distortion possibilities (see, for example, [39]) can be the reason of observed spectra deviation from the weak turbulence predictions. These results can be used for explanation of experimental data obtained in the wavetanks.…”

Ocean bottom pressure records from the Cascadia array and short surface gravity waves

“…This linear approximation holds up to f = 4 f PM , which gives f s = 1.4 Hz for the average wind speed of . The effects of long wave orbital currents on shorter waves [ Longuet‐Higgins and Stewart , ] are neglected here, but they could represent a less than 1 dB correction according to Korotkevich []. The empirical overlap integral (4) can be plotted as a function of: where C is the surface wave phase speed (see equation ).…”