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Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity

Published online by Cambridge University Press:  11 July 2002

SCOTT W. McCUE  and
LAWRENCE K. FORBES
SCOTT W. McCUE
Affiliation:
Department of Mathematics, University of Queensland, Queensland 4072, Australia Present address: Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
LAWRENCE K. FORBES
Affiliation:
Department of Mathematics, University of Queensland, Queensland 4072, Australia Present address: Department of Mathematics, University of Tasmania, GPO Box 252-37 Hobart 7001, Australia.
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Abstract

The free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 461 , 25 June 2002 , pp. 387 - 407
Copyright
© 2002 Cambridge University Press

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