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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: aviudez@cmima.csic.es
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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

Chaplygin, S. A. 1903 One case of vortex motion in fluid. Trans. Phys. Sect. Imperial Moscow Soc. Friends of Natural Sciences 11 (N2), 11–14.Google Scholar
Dritschel, D. G. & Viúdez, A. 2003 A balanced approach to modelling rotating stably-stratified geophysical flows. J. Fluid Mech. 488, 123–150.Google Scholar
Flierl, G. R., Stern, M. E. & Whitehead, J. A. 1983 The physical significance of modons: laboratory experiments and general integral constraints. Dyn. Atmos. Oceans 7, 233–264.Google Scholar
Hoskins, B. J., Draghici, I. & Davies, H. C. 1978 A new look at the 𝜔-equation. Q. J. R. Meterol. Soc. 104 (439), 31–38.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Meleshko, V. V. & van Heijst, G. J. F. 1994 On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid. J. Fluid Mech. 272, 157–182.Google Scholar
Rhines, P. B. & Young, W. R. 1983 How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133–145.Google Scholar
Velasco Fuentes, O. U. 2000 Evolution of a Lamb quadrupolar vortex. Fluid Dyn. Res. 26 (1), 13–33.Google Scholar
Wayne, C. E. 2011 Vortices and two-dimensional fluid motion. Notices of the AMS 58, 10–19.Google Scholar

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