The gravity waves created by a moving source in a fluid of finite depth
Authors:
A. K. Pramanik and M. Majumdar
Journal:
Quart. Appl. Math. 50 (1992), 437-449
MSC:
Primary 76B15
DOI:
https://doi.org/10.1090/qam/1178426
MathSciNet review:
MR1178426
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Abstract: The linear gravity waves created by a moving oscillatory source are considered in a fluid of finite uniform depth bounded on one side by a vertical cliff. The unsteady asymptotic waves are determined by Bliestien’s asymptotic expansion to the exact Fourier transform solution. Several physically interesting results are obtained. The fronts of each of the waves generated by the source are determined for all times and for all values of the parameters. The physical cause of the singularity of solution for certain values of the parameters is explained.
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A. K. Pramanik and S. R. Majumdar, Small amplitude free surface waves generated by moving oscillatory disturbances, J. Fluid Mech. 145, 405–415 (1984)
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T. R. Akylas, On the excitation of nonlinear water waves by a moving pressure distribution oscillating at resonant frequency, Phys. Fluid 27, 2803–2804 (1984)
N. Bliestien, Uniform asymptotic expansions of integrals with stationary points and nearby algebraic singularity, Comm. Pure Appl. Math. 19, 353 (1966)
L. Debnath and S. Rosenblat, The ultimate approach to the steady state in the generation of waves on a running stream, Quart. J. Mech. Appl. Math. 22, 221–233 (1969)
A. K. Pramanik and S. R. Majumdar, Small amplitude free surface waves generated by moving oscillatory disturbances, J. Fluid Mech. 145, 405–415 (1984)
P. Sarkar, Asymptotic analysis of waves due to oscillatory surface pressure over a sloping beach, SIAM J. Appl. Math. (3) 42, 532–541 (1982)
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Article copyright:
© Copyright 1992
American Mathematical Society
