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Nonlinear gravity–capillary standing waves in water of arbitrary uniform depth

Published online by Cambridge University Press:  20 April 2006

Jean-Marc Vanden-Broeck
Jean-Marc Vanden-Broeck
Affiliation:
Mathematics Department and Mathematics Research Center, University of Wisconsin-Madison, Madison, Wisconsin 53706
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Abstract

Gravity–capillary standing waves in water of arbitrary uniform depth are considered. The classical perturbation calculation yields unbounded coefficients for some critical values of the depth. In the present paper solutions valid near the first critical value of the depth are derived. A problem of non-uniqueness is discovered and discussed. It is shown that two solutions exist, one with higher frequency and one with lower frequency than the zeroth-order solution. They are found analytically at the critical value of the depth and numerically in an interval around it. Graphs of the results are included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 97 - 104
Copyright
© 1984 Cambridge University Press

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References

Concus, P. 1962 J. Fluid Mech. 14, 568.
Concus, P. 1964 J. Fluid Mech. 19, 264.
Chen, B. & Saffman, P. G. 1979 Stud. Appl. Maths. 60, 183.
Pierson, W. J. & Fife, P. 1961 J. Geophys. Res. 66, 163.
Schwartz, L. W. & VANDEN-BROECK, J.-M. 1979 J. Fluid Mech. 95, 119.
Tadjbakhsh, I. & Keller, J. B. 1960 J. Fluid Mech. 8, 422.
Vanden-Broeck, J.-M. & Schwartz, L. W. 1981 Phys. Fluids 24, 812.
Wilton, J. R. 1915 Phil. Mag. 29, 688.