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Resonant Interactions between Vortical Flows and Water Waves. Part II: Shallow Water
Author(s) -
Milewski P. A.
Publication year - 1995
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1995943225
Subject(s) - inviscid flow , conservative vector field , streamlines, streaklines, and pathlines , stream function , flow (mathematics) , free surface , vorticity , mechanics , vortex , waves and shallow water , surface (topology) , physics , potential flow , classical mechanics , surface wave , mathematics , compressibility , geometry , optics , thermodynamics
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.