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Exact solutions of asymmetric baroclinic quasi-geostrophic dipoles with distributed potential vorticity

Published online by Cambridge University Press:  12 April 2019

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

An exact solution of a baroclinic three-dimensional vortex dipole in geophysical flows with constant background rotation and constant background stratification is provided under the quasi-geostrophic (QG) approximation. The motion of the dipole is unsteady but the potential vorticity contours move rigidly. The vortex comprises three potential vorticity anomaly modes, with a radial dependence given by the spherical Bessel functions and with azimuthal and polar dependences given by the spherical harmonics. The first mode, or spherical mode, accounts for the horizontal asymmetry of the vortex dipole and curvature of the dipole’s horizontal trajectory. The second mode, or dipolar mode, accounts for the speed of displacement of the vortex dipole. A third mode, or vertical tilting mode, accounts for the dipole’s vertical asymmetry. The QG vertical velocity field has two contributions: the first one is octupolar and depends entirely on the dipolar mode, and the second one is dipolar and depends on the nonlinear interaction between dipolar and vertical tilting modes.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Quasi-geostrophic flows Vortex Flows: Vortex dynamics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , R1
Copyright
© 2019 Cambridge University Press 

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