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Resonant Generation of Finite‐Amplitude Waves by Flow Past Topography on a β‐Plane

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The forced Korteweg‐de Vries (fKdV) equation is the generic equation for resonant flow past an obstacle. However, for flow past topography on a β‐plane, the case when the upstream flow is uniform is anomalous in that there is no quadratic nonlinear term in the fKdV equation. Here we show that in this important case an alternative theory is required and obtain a new evolution equation, which has some similarities to the fKdV equation with two significant differences. These are that a small‐amplitude topography now produces finite‐amplitude waves and the flow response is limited by a wave breakdown characterized by an incipient flow reversal. Various numerical solutions are described.
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Document Type: Research Article

Affiliations: University of New South Wales

Publication date: February 1, 1993

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