Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-16T17:05:35.228Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave-source expansions for water of infinite depth in the presence of surface tension

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  26 February 2010

P. F. Rhodes-Robinson
P. F. Rhodes-Robinson
Affiliation:
Department of Mathematics, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand.
Get access

Abstract

In this paper two expansions are obtained by contour integration methods for the velocity potential describing two-dimensional time-harmonic surface waves due to a free-surface wave source on water of infinite depth in the presence of surface tension. First the series expansion at r = 0 is found and then the asymptotic expansion as Kr®¥, where K is the wave number for progressive waves and r the radial distance from the source. The corresponding expansions for the more important submerged wave source in terms of the radial distance from the image source in the free surface may then easily be deduced. The latter are required in a number of surface wave problems, particularly those of a short-wave asymptotic nature, and are also relevant in obtaining expansions for finite constant depth.

MSC classification

Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 67 - 76
Copyright
Copyright © University College London 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Rhodes-Robinson, P. F.. On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. II, III. Proc. Camb. Phil. Soc, 67 (1970), 443–468; 72 (1972), 83–94.CrossRefGoogle Scholar
Rhodes-Robinson, P. F.. Fundamental singularities in the theory of water waves with surface tension. Bull. Austral. Math. Soc, 2 (1970), 317–333.CrossRefGoogle Scholar
Rhodes-Robinson, P. F.. On surface waves in the presence of immersed vertical boundaries. I, II. Quart. J. Mech. Appl. Math., 32 (1979), 109–124; 125–133.CrossRefGoogle Scholar
Thome, R. C.. Multipole expansions in the theory of surface waves. Proc. Camb. Phil. Soc, 49 (1953), 707–716.Google Scholar
Ursell, F.. Short surface waves due to an oscillating immersed body. Proc. Roy. Soc. Ser. A, 220 (1953), 90–103.Google Scholar
Ursell, F.. The transmission of surface waves under surface obstacles. Proc Camb. Phil. Soc, 57 (1961), 638–668.CrossRefGoogle Scholar
Yu, Y. S. and Ursell, F.. Surface waves generated by an oscillating circular cylinder on water of finite depth: theory and experiment. J. Fluid Mech., 11 (1961), 529–551.CrossRefGoogle Scholar