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Flow structure beneath rotational water waves with stagnation points

Published online by Cambridge University Press:  06 January 2017

Roberto Ribeiro Jr ,
Paul A. Milewski  and
André Nachbin
Roberto Ribeiro Jr
Affiliation:
UFPR/Federal University of Paraná, Departamento de Matemática, Centro Politécnico, Jardim das Américas, Caixa Postal 19081, Curitiba, PR 81531-980, Brazil
Paul A. Milewski
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
André Nachbin*
Affiliation:
IMPA/National Institute of Pure and Applied Mathematics, Est. D. Castorina, 110, Rio de Janeiro, RJ 22460-320, Brazil
*
†Email address for correspondence: nachbin@impa.br
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Abstract

The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressure and particle paths can be found and mapped back to the physical domain. We find that the flow beneath the waves contains zero, one, two or three stagnation points in a frame moving with the wave speed, and describe the bifurcations between these flows. When the vorticity is sufficiently strong, the pressure in the flow and on the bottom boundary also has very different features from the usual irrotational wave case.

JFM classification

Wakes/Jets: Shear layers Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 792 - 814
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Copyright
© 2017 Cambridge University Press 

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