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Trapped edge waves in stratified rotating fluids: numerical and asymptotic results

Published online by Cambridge University Press:  14 November 2007

ALEXANDER T. I. ADAMOU ,
R. V. CRASTER  and
STEFAN G. LLEWELLYN SMITH
ALEXANDER T. I. ADAMOU
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
R. V. CRASTER
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
STEFAN G. LLEWELLYN SMITH
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla CA 92093-0411, USA
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Abstract

The existence of trapped edge waves in a rotating stratified fluid with non-constant topography is studied using asymptotic and numerical techniques. A refinement of the classical WKBJ method is employed that is uniform at both the shoreline and caustic, where the classical approximation is singular, and is also uniform over long distances from the shore. This approach requires the use of comparison equations and it is shown that the two used previously in the literature are asymptotically equivalent in terms of the wave amplitude, but have small differences in the predicted wave frequencies. These asymptotic results, and results using shallow-water theory, are then compared to results from a careful numerical study of the nonlinear differential eigenvalue problem, allowing their range of practical applicability to be assessed. This numerical approach is also used to investigate whether trapping occurs in non-trivial and realistic geometries in the internal gravity wave band, which has been an open question for some time.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 195 - 220
Copyright
Copyright © Cambridge University Press 2007

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