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Time-dependent critical layers in shear flows on the beta-plane

Published online by Cambridge University Press:  20 April 2006

Fred J. Hickernell
Fred J. Hickernell
Affiliation:
Department of Mathematics, University of Southern California, University Park, Los Angeles
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Abstract

The problem of a finite-amplitude free disturbance of an inviscid shear flow on the beta-plane is studied. Perturbation theory and matched asymptotics are used to derive an evolution equation for the amplitude of a singular neutral mode of the Kuo equation. The effects of time-dependence, nonlinearity and viscosity are included in the analysis of the critical-layer flow. Nonlinear effects inside the critical layer rather than outside the critical layer determine the evolution of the disturbance. The nonlinear term in the evolution equation is some type of convolution integral rather than a simple polynomial. This makes the evolution equation significantly different from those commonly encountered in fluid wave and stability problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 142 , May 1984 , pp. 431 - 449
Copyright
© 1984 Cambridge University Press

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