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Resonantly interacting solitary waves

Published online by Cambridge University Press:  11 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla
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Abstract

Resonant (phase-locked) interactions among three obliquely oriented solitary waves are studied. It is shown that such interactions are associated with the parametric end points of the singular regime for interactions between two solitary waves. The latter include regular reflexion at a rigid wall, which is impossible for ϕi < (3α)½ (ϕ = angle of incidence, α = amplitude/depth [Lt ] 1), and it is shown that the observed phenomenon of ‘Mach reflexion’ can be described as a resonant interaction in this regime. The run-up at the wall is calculated as a function of ϕi/(3α)½ and is found to have a maximum value of 4αd for ϕi = (3α)½. This same resonant interaction also describes diffraction of a solitary wave at a corner of internal angle π − ψi, −(3α)½, and suggests that a solitary wave cannot turn through an angle in excess of (3α)½ at a convex corner without separating or otherwise losing its identity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 1 , 20 January 1977 , pp. 171 - 179
Copyright
© 1977 Cambridge University Press

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References

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