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The Ekman flow and related problems: spectral theory and numerical analysis

Published online by Cambridge University Press:  21 April 2004

LEON GREENBERG  and
MARCO MARLETTA
LEON GREENBERG
Affiliation:
Dept. of Mathematics, University of Maryland, College Park, Maryland, MD 20740, U.S.A.
MARCO MARLETTA
Affiliation:
Dept. of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH
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Abstract

We consider singular block operator problems of the type arising in the study of stability of the Ekman boundary layer. The essential spectrum is located, and an analysis of the $L^2$ solutions of a related first order system of differential equations allows the development of a Titchmarsh–Weyl coefficient $M(\lambda)$. This, in turn, permits a rigorous analysis of the convergence of approximations to the spectrum arising from regular problems. Numerical results illustrate the theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 3 , May 2004 , pp. 719 - 764
Copyright
2004 Cambridge Philosophical Society

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