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A note on the steady two-dimensional flow of a stratified fluid over an obstacle

Published online by Cambridge University Press:  28 March 2006

R. Grimshaw
R. Grimshaw
Affiliation:
Mathematics Department, University of Melbourne
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Abstract

The steady two-dimensional flow of an inviscid incompressible fluid of variable density is considered in a long channel, bounded above by a rigid horizontal plane and below by an obstacle. For certain variations with height of the speed aud density in the incident stream, the governing equation is the reduced wave equation. Drazin & Moore (1967) have recently used this fact to develop a waveguide analogy. In this note the wave-guide analogy is further developed and several uniqueness theorems obtained. When the obstacle satisfies a certain convexity condition it is shown that the upstream conditions and the obstacle uniquely determine the flow; that is, there is no critical internal Froude number or obstacle height for which the problem fails to be well posed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 2 , 12 August 1968 , pp. 293 - 301
Copyright
© 1968 Cambridge University Press

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References

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