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Solitary waves in concentrated vortices

Published online by Cambridge University Press:  29 March 2006

S. Leibovich  and
J. D. Randall
S. Leibovich
Affiliation:
Department of Thermal Engineering, Cornell University, Ithaca., N.Y.
J. D. Randall
Affiliation:
Department of Thermal Engineering, Cornell University, Ithaca., N.Y.
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Abstract

A nonlinear integro-differential equation governing finite amplitude wave propagation on concentrated vortices is solved numerically. The solution to the Cauchy problem shows a solitary wave development qualitatively similar to solutions of the Korteweg–de Vries equation. A perturbation solution of the stationary form of the evolution equation confirms the unsteady calculation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 51 , Issue 4 , 22 February 1972 , pp. 625 - 635
Copyright
© 1972 Cambridge University Press

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References

Gardner, C. S., Greene, J.M., Kruskal, M.D. & Miura, R. M. 1967 Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19, 1095.Google Scholar
Leibovich, S. 1970 Weakly non-linear waves in rotating fluids. J. Fluid Mech. 42, 803.Google Scholar
Pritchard, W. G. 1970 Solitary waves in rotating fluids. J. Fluid Mech. 42, 61.Google Scholar
Randall, J. D. 1972 Ph.D. Thesis, Cornell University.
Zabusky, N. J. 1968 Solutions and bound states of the time-independent Schrödinger equation. Phys. Rev. 168, 124.Google Scholar