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On the behaviour of small disturbances in plane Couette flow

Published online by Cambridge University Press:  28 March 2006

A. P. Gallagher  and
A. McD. Mercer
A. P. Gallagher
Affiliation:
Department of Engineering Mathemataics, The Queen's University of Belfast
A. McD. Mercer
Affiliation:
Department of Engineering Mathemataics, The Queen's University of Belfast
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Abstract

The problem considered here is concerned with small disturbances of plane Couette flow. As is usual in such problems it is assumed that the disturbance velocities are sufficiently small to allow the Navier-Stokes equations to be linearized. There results a special case of the well-known Orr-Sommerfeld equation and this is solved by an exact method using a digital computer. The problem has previously been considered by several authors, mostly using approximate methods and their results have been compared where possible with those obtained here. It was possible to proceed to values of αR not in excess of 1000 (α being the wave-number of the disturbance and R the Reynolds number of the basic flow), and the results tend to confirm the belief that Couette flow is stable at all Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 1 , May 1962 , pp. 91 - 100
Copyright
© 1962 Cambridge University Press

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