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The stability of an evolving two-dimensional vortex sheet

Part of: Hydrodynamic stability

Published online by Cambridge University Press:  26 February 2010

D. W. Moore
D. W. Moore
Affiliation:
Department of Mathematics, Imperial College, London.
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Abstract

The stability of a two-dimensional vortex sheet against small disturbances in the plane of flow is examined. An integro-differential equation for the disturbances is derived and the possibility of solving it approximately is discussed. The approximation is equivalent to saying that short waves grow in a fashion determined by the local strength of the vortex sheet and it is shown that this need not be true throughout the evolution of the disturbance unless the growth rate is the same everywhere. It is possible for the disturbance on a distant part of the vortex sheet to control what happens locally, if the disturbance on the distant part is growing more rapidly. The approximate theory is applied to the tightly-wound spirals of aerodynamic interest and these are shown to be stable.

MSC classification

Secondary: 76E99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 35 - 44
Copyright
Copyright © University College London 1976

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