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Resonant Forcing of Barotropic Coastally Trapped Waves

R. GrimshawSchool of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia

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Abstract

The interaction of a longshore current with a longshore topographic feature is investigated in the barotropic case. It is shown that near resonance, when a long-wave speed is close to zero (in a fixed reference frame), there is enhanced generation of upstream and downstream coastally trapped waves. An evolution equation of the the KdV-type is derived to describe the resonant behavior, and numerical solutions are discussed for a range of parameters describing the forcing terms, the detuning term and dissipation. The analogous situation of resonant generation due to wind stress is developed in an appendix.

Abstract

The interaction of a longshore current with a longshore topographic feature is investigated in the barotropic case. It is shown that near resonance, when a long-wave speed is close to zero (in a fixed reference frame), there is enhanced generation of upstream and downstream coastally trapped waves. An evolution equation of the the KdV-type is derived to describe the resonant behavior, and numerical solutions are discussed for a range of parameters describing the forcing terms, the detuning term and dissipation. The analogous situation of resonant generation due to wind stress is developed in an appendix.

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