Weakly nonlinear internal wave fronts trapped in contractions

S. R. Clarke, R. H.J. Grimshaw

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The propagation of weakly nonlinear, long internal wave fronts in a contraction is considered in the transcritical limit as a model for the establishment of virtual controls. It is argued that the appropriate equation to describe this process is a variable coefficient Korteweg-de Vries equation. The solutions of this equation are then considered for compressive and rarefaction fronts. Rarefaction fronts exhibit both normal and virtual control solutions. However, the interaction of compressive fronts with contractions is intrinsically unsteady. Here the dynamics take two forms, interactions with the bulk of the front and interactions with individual solitary waves separating off from a front trapped downstream of the contraction.

Original languageEnglish
Pages (from-to)323-345
Number of pages23
JournalJournal of Fluid Mechanics
Publication statusPublished - 1 Jan 2000

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