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Steady two-dimensional flow of fluid of variable density over an obstacle

Published online by Cambridge University Press:  28 March 2006

P. G. Drazin  and
D. W. Moore
P. G. Drazin
Affiliation:
Mathematics Department, University of Bristol
D. W. Moore
Affiliation:
Institute for Space Studies, New York City
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Abstract

A model of airflow over a mountain is treated mathematically in this paper. The fluid is inviscid, incompressible and of variable density. The flow is in a long channel, bounded above by a rigid horizontal lid and below by an obstacle. The variation with height of the horizontal velocity and of the density is specified far upstream. The details of flow are examined for particular conditions upstream which lead to a linear vorticity equation, although the non-linear inertial terms in the Euler equations of motion are exactly represented. In this case the flow is described by the superposition of solutions of some diffraction problems. Classical techniques of diffraction theory are then used to demonstrate the existence and some general properties of solutions for steady flow. Thus a steady solution is always possible if no restriction is placed on the amount of energy available to drive the flow, that is to say there is no critical internal Froude number (measuring the dynamical effect of buoyancy) for the existence of a steady flow. Finally the flows past a dipole and a vertical wall are computed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 2 , 8 May 1967 , pp. 353 - 370
Copyright
© 1967 Cambridge University Press

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