Abstract

Any weak, steady vortical flow is a solution, to leading order, of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of long irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic and have comparable length scales, resonant interactions can occur between the various components of the flow. The interaction is described by two coupled Korteweg-de Vries equations and a two-dimensional streamfunction equation.

Original languageEnglish
Pages (from-to)225-256
Number of pages32
JournalStudies in Applied Mathematics
Volume94
Issue number3
DOIs
Publication statusPublished - 1 Apr 1995

Fingerprint

Water waves
Shallow Water
Water Waves
Surface waves
Korteweg-de Vries equation
Gravity waves
Steady flow
Surface Waves
Interaction
Free Surface
Wave propagation
Water
Gravity Waves
Fluids
Streamlines
Steady Flow
Korteweg-de Vries Equation
Length Scale
Horizontal
Propagation

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Resonant Interactions between Vortical Flows and Water Waves. Part II : Shallow Water. / Milewski, P. A.

In: Studies in Applied Mathematics, Vol. 94, No. 3, 01.04.1995, p. 225-256.

Research output: Contribution to journalArticle

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