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Nonlinear stern waves

Published online by Cambridge University Press:  19 April 2006

J.-M. Vanden-Broeck
J.-M. Vanden-Broeck
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
Present address: Department of Mathematics, Stanford University, Stanford, CA 94305.
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Abstract

Steady two-dimensional potential flow past a semi-infinite flat-bottomed body is considered. This stern flow is assumed to separate tangentially from the body. Gravity waves of finite amplitude occur on the free surface. An exact relation between the amplitude of these waves and the Fronde number F is derived. It shows that these waves can exist only for F greater than the value F* = 2·23. This is slightly less than the value Fc = 2·26 at which breaking occurs. For F slightly larger than F*, the steepness is a multi-valued function of F, indicating the existence of more than one solution for these values of F. In addition, a numerical scheme based on an integro-differential equation formulation is derived to solve the problem in the fully nonlinear case. The shape of the free surface profile is computed for different values of F. As a check on the numerical results, they are shown to satisfy the exact relation between steepness and the Froude number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 3 , 13 February 1980 , pp. 603 - 611
Copyright
© 1980 Cambridge University Press

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References

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