Hostname: page-component-6d856f89d9-72csx Total loading time: 0 Render date: 2024-07-16T07:30:04.742Z Has data issue: false hasContentIssue false
  • English
  • Français

Large amplitude surface waves

Published online by Cambridge University Press:  12 April 2006

M. I. G. Bloor
M. I. G. Bloor
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, England
Get access Rights & Permissions [Opens in a new window]

Abstract

A transformation technique is used to solve the problem of steady nonlinear surface waves where the restoring force is either gravity or surface tension. An exact nonlinear integro-differential equation is found which yields known approximate solutions. Extensions to the method to account for more complicated geometries are also illustrated. The equation is solved numerically and results in agreement with previous solutions are obtained. In the case of capillary waves, the existence of two types of wave of greatest height is clearly indicated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 1 , 16 January 1978 , pp. 167 - 179
Copyright
© 1978 Cambridge University Press

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

Byatt-Smith, J. 1969 Univ. Calif., Coll. Engng Rep. AS-69-3.
Cokelet, E. D. 1977 Phil. Trans. Roy. Soc. (in press).
Crapper, G. D. 1957 J. Fluid Mech. 2, 532.
John, F. 1953 Comm. Pure. Appl. Math. 6, 497.
Kinnersley, W. 1976 J. Fluid Mech. 77, 229.
Kinsman, B. 1965 Wind Waves, Their Generation and Propagation on the Ocean Surface. Prentice Hall.
Levi-Civita, T. 1925 Math. Ann. 93, 264.
Long, R. R. 1956 Tellus 8, 1460.
Longuet-Higgins, M. S. 1975 Proc. Roy. Soc. A 342, 157.
Michell, J. H. 1893 Phil. Mag. (5), 36, 430.
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn. Macmillan.
Nekrasov, A. I. 1921 Isv. Ivanovo-Voznesensk Politekhn. Inst. 3, 52.
Schwartz, L. W. 1974 J. Fluid Mech. 62, 553.
Stokes, G. G. 1847 Trans. Camb. Phil. Soc. 8, 441.
Thomas, J. W. 1968 Mathematika 15, 139.
Thomas, J. W. 1975 Quart. Appl. Math. 32, 403.
Wehausen, J. V. 1965 In Research Frontiers in Fluid Dynamics (ed. R. J. Seager & G. Temple), p. 534. Interscience.
Wehausen, J. V. & Laitone, E. V. 1960 Handbuch der Physik, vol. 9 (ed. S. Flügge), p. 446. Springer.