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On Rossby waves modified by basic shear, and barotropic instability

Published online by Cambridge University Press:  20 April 2006

P. G. Drazin ,
D. N. Beaumont  and
S. A. Coaker
P. G. Drazin
Affiliation:
School of Mathematics, University of Bristol
D. N. Beaumont
Affiliation:
School of Mathematics, University of Bristol Present address: British Gas, London Research Station, Michael Road, London SW6 2AD.
S. A. Coaker
Affiliation:
School of Mathematics, University of Bristol
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Abstract

The eigenvalue problem of Kuo governing the linear stability of a parallel zonal flow of an inviscid incompressible fluid on a β-plane is treated in this paper. First, a synthesis of the known properties of the normal modes is presented, as a short summary. The rest of the paper is a study of the properties of one of the classes of stable modes, namely Rossby waves modified by the basic shear. These modes are found as the solution of the inverse of a regular Sturm–Liouville problem. Several asymptotic results for small and for increasing values of the basic shear (i.e. equivalently for large and decreasing values of β) are found for quite general velocity profiles. These are illustrated by some numerical calculations of the wave characteristics for a few particular basic velocity profiles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 439 - 456
Copyright
© 1982 Cambridge University Press

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