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Small-amplitude free-surface waves generated by moving oscillatory disturbances

Published online by Cambridge University Press:  20 April 2006

A. K. Pramanik  and
S. R. Majumdar
A. K. Pramanik
Affiliation:
Department of Applied Mathematics, Calcutta University, India
S. R. Majumdar
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Alberta, Canada
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Abstract

The problem of capillary–gravity waves generated by certain moving oscillatory surface-pressure distributions is investigated. The main difficulty of the problem lies in finding the real roots of the modified frequency equations. This is dealt with by the use of certain geometric considerations. The critical condition that results from the formation of double roots of the modified frequency equations is represented as a surface. This surface divides the whole space into several distinct regions. For points in different regions the propagation of waves is different. The waves are determined in all cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 405 - 415
Copyright
© 1984 Cambridge University Press

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References

Debnath, L. & Rosenblat, S. 1969 The ultimate approach to the steady state in the generation of waves on a running stream. Q. J. Mech. Appl. Maths 22, 221–233.Google Scholar
Kaplan, P. 1957 The waves generated by the forward motion of oscillatory pressure distribution. In Proc. 5th Midwest Conf. Fluid Mech., pp. 316–329.
Lighthill, M. J. 1962 Fourier Analysis and Generalised Functions. Cambridge University Press.
Magnuson, A. H. 1977 The disturbance produced by an oscillatory pressure distribution in uniform translation on the surface of a liquid. J. Engng Maths 2, 121–137.Google Scholar
Pramanik, A. K. 1980 Capillary—gravity waves produced by a moving pressure distribution. Z. angew. Math. Phys, 31, 174–180.Google Scholar
Stoker, J. J. 1957 Water Waves. Interscience.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley-Interscience.