A note on the steady two-dimensional flow of a stratified fluid over an obstacle
- 12 July 1968
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 33 (02) , 293-301
- https://doi.org/10.1017/s002211206800131x
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.Keywords
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