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The jet from a horizontal slot at large Froude number

Published online by Cambridge University Press:  24 October 2008

G. Keady
G. Keady
Affiliation:
Department of Mathematics, University of Melbourne, Australia
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The two-dimensional flow in a jet, falling under gravity from a slot in a horizontal plane, is studied. The fluid is considered to be incompressible and inviscid; the flow is taken to be irrotational; and the reciprocal ε of the Froude number is considered to be small. By taking the complex potential as the independent variable we overcome the difficulty that the boundary geometry is not known in advance. The method of matched asymptotic expansions is applied. The first two terms of an inner asymptotic expansion and the first three of an outer one are found: the inner expansion is valid above and near the slot, but is inappropriate far downstream, while the outer expansion is valid far downstream, but fails to satisfy the conditions upstream. The two expansions are matched and ‘composite’ approximations, covering the whole flow field, are derived.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 3 , May 1973 , pp. 515 - 529
Copyright
Copyright © Cambridge Philosophical Society 1973

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