dorsal/arxiv
View SchemaOn the Doppler distortion of the sea-wave spectra
| Authors | Alexander O. Korotkevich |
|---|---|
| Categories | |
| ArXiv ID | physics/0110009 |
| URL | https://arxiv.org/abs/physics/0110009 |
| DOI | 10.1016/j.physd.2008.04.005 |
| Journal | A.O. Korotkevich, On the Doppler distortion of the sea-wave spectra, Physica D, vol. 237, issue 21, pp. 2767-2776 (2008) |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Discussions on a form of a frequency spectrum of wind-driven sea waves just above the spectral maximum have continued for the last three decades. In 1958 Phillips made a conjecture that wave breaking is the main mechanism responsible for the spectrum formation (Phillips, 1958). That leads to the spectrum decay $\sim \omega^{-5}$, where $\omega$ is the frequency of waves. There is a contradiction between the numerous experimental data and this spectrum. Experiments frequently show decay $\sim\omega^{-4}$ (Toba, 1973),(Donelan et al, 1985), and (Hwang et al, 1999). There are several ways of the explanation of this phenomenon. One of them (proposed by Banner (Banner, 1990)) takes into account the Doppler effect due to surface circular currents generated by underlying waves in the Phillips model. In this article the influence of the Doppler effect on an arbitrary averaged spectrum is considered using both analytic and numerical approaches. Although we mostly concentrated on the very important case of Phillips model the developed technique and general formula can be used for the analysis of other spectra. For the particular case of Phillips spectra we got analytic asymptotics in the vicinity of spectral maximum and for high frequencies. Results were obtained for two most important angular dependences of the spectra: isotropic and strongly anisotropic. Together with the analytic investigation we performed numerical calculations in a wide range of frequencies. Both high and low frequency asymptotics are in very good agreement with the numerical results. It was shown that at least at low frequencies correction to the spectrum due to the Doppler shift is negligible. At high frequencies there is an asymptotic with tail $\sim \omega^{-3}$.
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"abstract": "Discussions on a form of a frequency spectrum of wind-driven sea waves just\nabove the spectral maximum have continued for the last three decades. In 1958\nPhillips made a conjecture that wave breaking is the main mechanism responsible\nfor the spectrum formation (Phillips, 1958). That leads to the spectrum decay\n$\\sim \\omega^{-5}$, where $\\omega$ is the frequency of waves. There is a\ncontradiction between the numerous experimental data and this spectrum.\nExperiments frequently show decay $\\sim\\omega^{-4}$ (Toba, 1973),(Donelan et\nal, 1985), and (Hwang et al, 1999). There are several ways of the explanation\nof this phenomenon. One of them (proposed by Banner (Banner, 1990)) takes into\naccount the Doppler effect due to surface circular currents generated by\nunderlying waves in the Phillips model.\n In this article the influence of the Doppler effect on an arbitrary averaged\nspectrum is considered using both analytic and numerical approaches. Although\nwe mostly concentrated on the very important case of Phillips model the\ndeveloped technique and general formula can be used for the analysis of other\nspectra.\n For the particular case of Phillips spectra we got analytic asymptotics in\nthe vicinity of spectral maximum and for high frequencies. Results were\nobtained for two most important angular dependences of the spectra: isotropic\nand strongly anisotropic. Together with the analytic investigation we performed\nnumerical calculations in a wide range of frequencies. Both high and low\nfrequency asymptotics are in very good agreement with the numerical results.\n It was shown that at least at low frequencies correction to the spectrum due\nto the Doppler shift is negligible. At high frequencies there is an asymptotic\nwith tail $\\sim \\omega^{-3}$.",
"arxiv_id": "physics/0110009",
"authors": [
"Alexander O. Korotkevich"
],
"categories": [
"physics.geo-ph",
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"doi": "10.1016/j.physd.2008.04.005",
"journal_ref": "A.O. Korotkevich, On the Doppler distortion of the sea-wave\n spectra, Physica D, vol. 237, issue 21, pp. 2767-2776 (2008)",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "On the Doppler distortion of the sea-wave spectra",
"url": "https://arxiv.org/abs/physics/0110009"
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