Small-amplitude internal waves due to an oscillatory pressure
Author:
N. C. Mahanti
Journal:
Quart. Appl. Math. 37 (1979), 92-97
MSC:
Primary 76C10; Secondary 35Q99
DOI:
https://doi.org/10.1090/qam/530673
MathSciNet review:
530673
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Abstract: The initial-value problem of waves in superposed fluids which are otherwise unlimited due to an axisymmetrical oscillatory pressure is solved by the method of integral transforms. The wave integral representing interfacial displacement is evaluated in an asymptotic form that remains uniformly valid through the transition zone.
J. J. Stoker, Water waves, New York, Interscience (1957)
- John V. Wehausen and Edmund V. Laitone, Surface waves, Handbuch der Physik, Vol. 9, Part 3, Springer-Verlag, Berlin, 1960, pp. 446–778. MR 0119656
- A. R. Sen, Deep-water surface waves due to arbitrary periodic pressures, Proc. Nat. Inst. Sci. India Part A 28 (1962), 612–631. MR 148307
L. Debnath, An asymptotic treatment of the transient development of axisymmetric surface waves, Appl. Sci. Res. 21, 24–36 (1969)
L. Debnath, On transient development of internal waves in stratified ocean, Indian J. Pure Appl. Math. 1, 372–388 (1970)
N. C. Mahanti, Small amplitude surface waves due to an oscillatory pressure. Israel J. Tech. 15(3) (1978) (to appear)
B. L. van der Waerden, On the method of saddle points, Appl. Sci. Res. 2B, 33–45 (1951)
A. Erdélyi et al., Higher transcendental functions, 2, New York, McGraw-Hill (1953)
- John W. Miles, Transient gravity wave response to an oscillating pressure, J. Fluid Mech. 13 (1962), 145–150. MR 138285, DOI https://doi.org/10.1017/S0022112062000579
J. J. Stoker, Water waves, New York, Interscience (1957)
J. V. Wehausen and E. V. Laitone, Surface waves, in Handbuch der Physik IX, Springer, Berlin (1960)
A. R. Sen, Deep-water surface waves due to arbitrary periodic pressures, Proc. Nat. Inst. Sci. India 28, 612–631 (1962)
L. Debnath, An asymptotic treatment of the transient development of axisymmetric surface waves, Appl. Sci. Res. 21, 24–36 (1969)
L. Debnath, On transient development of internal waves in stratified ocean, Indian J. Pure Appl. Math. 1, 372–388 (1970)
N. C. Mahanti, Small amplitude surface waves due to an oscillatory pressure. Israel J. Tech. 15(3) (1978) (to appear)
B. L. van der Waerden, On the method of saddle points, Appl. Sci. Res. 2B, 33–45 (1951)
A. Erdélyi et al., Higher transcendental functions, 2, New York, McGraw-Hill (1953)
J. W. Miles, Transient gravity wave response to an oscillatory pressure, J. Fluid Mech. 13, 145–150 (1962)
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Article copyright:
© Copyright 1979
American Mathematical Society
