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Solitary waves on a vorticity layer

Published online by Cambridge University Press:  26 April 2006

F. J. Higuera  and
J. Jiménez
F. J. Higuera
Affiliation:
E.T.S. Ingenieros Aeronáuticos, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
J. Jiménez
Affiliation:
E.T.S. Ingenieros Aeronáuticos, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
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Abstract

Contour dynamics methods are used to determine the shapes and speeds of planar, steadily propagating, solitary waves on a two-dimensional layer of uniform vorticity adjacent to a free-slip plane wall in an, otherwise irrotational, unbounded incompressible fluid, as well as of axisymmetric solitary waves propagating on a tube of azimuthal vorticity proportional to the distance to the symmetry axis. A continuous family of solutions of the Euler equations is found in each case. In the planar case they range from small-amplitude solitons of the Benjamin–Ono equation to large-amplitude waves that tend to one member of the touching pair of counter-rotating vortices of Pierrehumbert (1980), but this convergence is slow in two small regions near the tips of the waves, for which an asymptotic analysis is presented. In the axisymmetric case, the small-amplitude waves obey a Korteweg–de Vries equation with small logarithmic corrections, and the large-amplitude waves tend to Hill's spherical vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 264 , 10 April 1994 , pp. 303 - 319
Copyright
© 1994 Cambridge University Press

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