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Topographic waves in open domains. Part 1. Boundary conditions and frequency estimates

Published online by Cambridge University Press:  26 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

The problem is considered of topographic waves propagating on depth gradients in rotating domains. A variational principle is derived for the eigenfunctions and eigenfrequencies of normal modes on a domain, and applied to subdomains of the whole domain. Considering suitable boundary conditions on the open boundary between the subdomain and the remainder of the whole domain gives upper and lower bounds and estimates for the frequencies of normal modes localized in the subdomain without the complication of solving over the whole domain. It is shown that applying a zero-mass-flux condition at the open boundary leads to a lower bound on the frequency whereas requiring a particular form of the energy flux to vanish identically at each point of the boundary provides an upper bound.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 69 - 76
Copyright
© 1989 Cambridge University Press

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