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On the generation of water waves at an inertial surface

Published online by Cambridge University Press:  17 February 2009

P. F. Rhodes-Robinson
P. F. Rhodes-Robinson
Affiliation:
Department of Mathematics, Victoria University of Wellington, New Zealand.
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Abstract

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In this paper we develop the Laplace-transform method to solve initial-value problems for the velocity potential describing the generation of infinitesimal capillary-gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles. The two principal problems considered are the forced motions due to a submerged wave source and an immersed vertical plane wave-maker, which begin to operate in a time-dependent manner at a given instant. The transformed potentials are calculated using techniques similar to those which are effective in traditional time-harmonic problems with a free surface. The steady-state development in the time-harmonic example taken demonstrates the existence of outgoing progressive waves under any inertial surface, in contrast to the case of no surface tension when such waves cannot propagate under an inertial surface that is too heavy. The solution is also noted of the Cauchy-Poisson problem for the free motion flowing an intial elevation of the inertial surface, which is obtained by the same method.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 3 , January 1984 , pp. 366 - 383
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Blake, J. R. and Cerone, P., “A note on the impulse due to a vapour bubble near a boundary”. J. Austral. Math. Soc. Ser. B 23 (1982), 383–393.CrossRefGoogle Scholar
[2]Finkelstein, A. B., “The initial-value problem for transient water waves”, Comm. Pure Appl. Math. 10 (1957), 511–522.CrossRefGoogle Scholar
[3]Havelock, T. H., “Forced surface waves on water”, Philos. Mag. 8 (1929), 569–576.CrossRefGoogle Scholar
[4]Kennard, E. H., “Generation of surface waves by a moving partition”. Quart. Appl. Math. 7 (1949), 303–312.CrossRefGoogle Scholar
[5]Peters, A. S., “The effect of a floating mat on water waves”, Comm. Pure App. Math. 3 1950), 319–354.CrossRefGoogle Scholar
[6]Rhodes-Robinson, P. F., “On the forced surface waves due to a vertical wave-maker in the presence of surface tension”, Proc. Cambridge Philos. Soc. 70 (1971), 323–337.CrossRefGoogle Scholar
[7]Rhodes-Robinson, P. F., “On waves at an interface between two liquids”, Math. Proc. Cambridge Philos. Soc. 88 (1980), 183–191.CrossRefGoogle Scholar
[8]Rhodes-Robinson, P. F., “Note on the reflexion of water waves at a wall in the presence of surface tension”, Math. Proc. Cambridge Philos. Soc. 92 (1982), 369–373.CrossRefGoogle Scholar
[9]Rhodes-Robinson, P. F., “Note on the effect of surface tension on water waves at an inertial surface”, J. Fluid Mech. 125 (1982), 375–377.CrossRefGoogle Scholar
[10]Thorne, R. C., “Multipole expansions in the theory of surface waves”, Proc. Cambridge Philos. Soc. 49 (1953), 707–716.CrossRefGoogle Scholar
[11]Wehausen, J. V. and Laitone, E. V., “Surface waves”, in Handbuch der Physik 9, (ed. Flügge, S.), (Springer-Verlag, Berlin, Göttingen. Heidelberg, 1960), 446–778.Google Scholar
[12]Weitz, M. and Keller, J. B., “Reflection of water waves from floating ice in water of finite depth”, Comm. Pure Appl. Math. 3 (1950). 305–318.CrossRefGoogle Scholar