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Ploughing flows

Published online by Cambridge University Press:  01 October 1998

E. O. TUCK  and
J.-M. VANDEN-BROECK
E. O. TUCK
Affiliation:
The University of Adelaide, Australia
J.-M. VANDEN-BROECK
Affiliation:
Department of Mathematics and Center for the Mathematical Sciences, University of Wisconsin-Madison, Wisconsin, USA
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Abstract

A semi-infinite body, modelling the leading edge of a cutting tool or submerged hydrofoil, lies beneath a free surface in a uniform stream of infinitely-deep inviscid incompressible fluid flowing steadily under gravity. The body has horizontal upper and lower surfaces. The oncoming flow is partly diverted over, and partly under the body. The flow in that portion that travels over the body can be supercritical or subcritical. When it is supercritical it approaches a stream of some (to be determined) speed in a channel of some (to be determined) depth. When it is subcritical, there is also a train of waves on that stream, whose amplitude is also to be determined. Semi-analytic high-speed and low-speed solutions are obtained, and a numerical solution for finite speeds. There is a ‘forbidden’ intermediate speed range, within which steady flow may not be possible.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 9 , Issue 5 , October 1998 , pp. 463 - 483
Copyright
1998 Cambridge University Press

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