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Azimuthal-mode solutions of two-dimensional Euler flows and the Chaplygin–Lamb dipole

Published online by Cambridge University Press:  28 November 2018

A. Viúdez Open the ORCID record for A. Viúdez [Opens in a new window]
A. Viúdez*
Affiliation:
Department of Physical Oceanography and Technology, Institute of Marine Sciences, CSIC, Barcelona 08003, Spain
*
†Email address for correspondence: [email protected]
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Abstract

Exact solutions for multipolar azimuthal-mode vortices in two-dimensional Euler flows are presented. Flow solutions with non-vanishing far-field velocity are provided for any set of azimuthal wavenumbers $m$ and arbitrary number $n$ of vorticity shells. For azimuthal wavenumbers $m=0$ and $m=1$, the far-field velocity is a rigid motion and unsteady flow solutions with vanishing far-field velocity are obtained by means of a time-dependent change of reference frame. Addition of these first two modes, in the case of $n=1$, results in a particular Chaplygin–Lamb (C–L) dipole, with continuous and vanishing vorticity at the vortex boundary. Numerical simulations suggest that this particular C–L dipole is stable.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , R1
Copyright
© 2018 Cambridge University Press 

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References

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