Frequency Down-Shift Through Self Modulation and Breaking
We simulate the development of a moderately steep wavetrain, using evolution equations correct to fourth order in the wave steepness(see Dysthe (1979) and Lo and Mei (1985)), with an added term simulating effects of wave breaking. It is found that the breaking damps the developing sidebands selectively, such that the most unstable lower sideband comes out of the modulation-breaking process being the dominant one. The reason for this, in our opinion, is the tendency towards spatial localization of the part of the wavetrain contributing to the upper sidebands. This “high-frequency” part of the signal seems to concentrate around the steepest portions of the wavetrain, where breaking occurs. This is found both in our simulations and in experimental records (Melville 1983).
KeywordsModulational Instability Wave Breaking Carrier Wave Wave Steepness Spectral Development
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- Trulsen, K. 1989 (Master thesis.) University of Tromso.Google Scholar