Asymptotic analysis of surface waves due to oscillatory wave maker
Author:
M. S. Faltas
Journal:
Quart. Appl. Math. 46 (1988), 489-494
MSC:
Primary 76B15
DOI:
https://doi.org/10.1090/qam/963584
MathSciNet review:
963584
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Abstract: The initial value problem of surface waves generated by a harmonically oscillating vertical wave-maker immersed in an infinite incompressible fluid of finite constant depth is presented. The resulting motion is investigated using the generalized function method, and an asymptotic analysis for large times and distances is given for the free surface elevation.
T. H. Havelock, Forced surface waves on water, Philos. Mag. 8, 569 (1929)
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L. Debnath and S. Rosenblat, The ultimate approach to the steady state in the generation of waves on running stream, Quart. J. Mech. Appl. Math. 22, 221 (1969)
M. J. Lighthill, Fourier analysis and generalized functions, Cambridge University Press, 1962
- E. T. Copson, Asymptotic expansions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 55, Cambridge University Press, New York, 1965. MR 0168979
T. H. Havelock, Forced surface waves on water, Philos. Mag. 8, 569 (1929)
P. F. Rhodes-Robinson, On the forced surface waves due to a vertical wave-maker in the presence of surface tension, Proc. Cambridge Philos. Soc. 70, 323–337 (1971)
A. K. Pramanik, Waves created against a vertical cliff—a uniform asymptotic solution, Math. Proc. Cambridge Philos. Soc. 83, 321–328 (1978)
L. Debnath and U. Basu, Capillary-gravity waves against a vertical cliff, Indian J. Math. 26, 49 (1984)
L. Debnath and S. Rosenblat, The ultimate approach to the steady state in the generation of waves on running stream, Quart. J. Mech. Appl. Math. 22, 221 (1969)
M. J. Lighthill, Fourier analysis and generalized functions, Cambridge University Press, 1962
E. T. Copson, Asymptotic Expansions, Cambridge University Press, 1965
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Article copyright:
© Copyright 1988
American Mathematical Society
