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Resonant generation of finite-amplitude waves by the uniform flow of a uniformly rotating fluid past an obstacle

Published online by Cambridge University Press:  26 February 2010

R. Grimshaw  and
Z. Yi
R. Grimshaw
Affiliation:
Department of Mathematics, Monash University, Clayton, Vic. 3168, Australia.
Z. Yi
Affiliation:
National Research Centre for Marine Environment, Forecasts, Hai Dian Division, Beijing, China.
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Abstract

In a previous paper (Grimshaw, 1990a) we showed that the resonant, or critical, flow of a rotating fluid past an axisymmetric obstacle placed on the axis of a cylindrical tube is described by a forced Korteweg-de Vries equation for the amplitude of the dominant resonant mode. Here we show that in the anomalous but important case when the oncoming flow is uniform with uniform angular velocity a different theory is required which leads to an evolution equation describing finite-amplitude waves. Some numerical solutions of this equation are described.

Type
Research Article
Information
Mathematika , Volume 40 , Issue 1 , June 1993 , pp. 30 - 50
Copyright
Copyright © University College London 1993

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