The Mechanism for Frequency Downshift in Nonlinear Wave Evolution

Norden E. Huang, Steven R. Long, Zheng Shen

Research output: Contribution to journalArticlepeer-review

269 Scopus citations

Abstract

Abstract. It has long been recognized that the frequency downshift in the wave field evolution is a consequence of nonlinear wave-wave interactions and that the frequency downshift is also necessary for the wind wave field to grow. Yet the detailed mechanism for the frequency change is still unknown: Is the process continuous and gradual? Or, is the frequency of a wave train varying gradually and continuously? Recently, Huang et al. (1995) found that the frequency downshift for a narrow band wave train is through wave fusion, an event described as two waves merging to form one wave, or n waves merging to form n-1 waves. The process was seen tobe local, abrupt, and discrete. Such an event cannot be studied by the traditional Fourier analysis. Using a Hilbert transform to produce the phase-amplitude diagram and the Hilbert Spectrum, we found that in addition to the narrow band waves, the wave fusion event could occur in finite band widths and wind wave fields as well; and it is indeed the mechanism responsible for the frequency downshift in nonlinear wave evolution in general. Specifically, the frequency downshift is an accumulation of wave fusion events, which is also the same phenomena of the "lost crest" observed by Lake and Yuen (1978), and the "crest pairing" observed by Ramamonjiarisoa and Mollo-Christensen (1979). We have made quantitative measure of this fusion through Hilbert analysis techniques. Other than the fusion process, the local frequency can have small variations due to the amplitude modulations. Because of the abrupt and discrete localized variations of wave frequency, a new paradigm is needed to describe the nonlinear wave evolution processes.

Original languageEnglish
Pages (from-to)59-117,117A,117B,117C
JournalAdvances in Applied Mechanics
Volume32
Issue numberC
DOIs
StatePublished - 1996

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