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Splash formation at the nose of a smoothly curved body in a stream

Published online by Cambridge University Press:  17 February 2009

E. O. Tuck  and
S. T. Simakov
E. O. Tuck
Affiliation:
Department of Applied Mathematics, University of Adelaide, SA 5005, Australia.
S. T. Simakov
Affiliation:
Department of Applied Mathematics, University of Adelaide, SA 5005, Australia.
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Abstract

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In two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 4 , April 1999 , pp. 421 - 436
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Birkhoff, G. and Zarantonello, E., Jets, Wakes and Cavities (Academic Press, New York, 1957).Google Scholar
[2]Brodetsky, S., “Discontinuous fluid motion past circular and elliptic cylinders”, Proc. R. Soc. Lond. A102 (1923) 542.Google Scholar
[3]Courant, R., Partial Differential Equations (Interscience Publishers, New York, 1962).Google Scholar
[4]Dagan, G. and Tulin, M. P., “Two-dimensional free-surface gravity flow past blunt bodies”, J. Fluid Mech. 51 (1972) 529.CrossRefGoogle Scholar
[5]Tuck, E. O. and Vanden-Broeck, J.-M., “Ploughing flows”, European J. Appl. Math. (1998) in press.CrossRefGoogle Scholar
[6]Vanden-Broeck, J.-M., “The influence of surface tension on cavitating flow past a curved obstacle” J. Fluid Mech. 133 (1983) 255.CrossRefGoogle Scholar