Model equation for nonlinear wavelength selection and amplitude evolution of frontal waves

M. Ghil*, N. Paldor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study a model equation describing the temporal evolution of nonlinear finite-amplitude waves on a density front in a rotating fluid. The linear spectrum includes an unstable interval where exponential growth of the amplitude is expected. It is shown that the length scale of the waves in the nonlinear situation is determined by the linear instabilities; the effect of the nonlinearities is to limit the amplitude's growth, leaving the wavelength unchanged. When linearly stable waves are prescribed as initial data, a short interval of rapid decrease in amplitude is encountered first, followed by a transfer of energy to the unstable part of the spectrum, where the fastest growing mode starts to dominate. A localized disturbance is broken up into its Fourier components, the linearly unstable modes grow at the expense of all other modes, and final amplitudes are determined by the nonlinear term. Periodic evolution of linearly unstable waves in the nonlinear situation is also observed. Based on the numerical results, the existence of low-order chaos in the partial differential equation governing weakly nonlinear wave evolution is conjectured.

Original languageEnglish
Pages (from-to)471-496
Number of pages26
JournalJournal of Nonlinear Science
Volume4
Issue number6
StatePublished - Nov 1994
Externally publishedYes

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