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Steady solutions of quasi-geostrophic flows in basins, gulfs and channels on a β-plane

Published online by Cambridge University Press:  10 October 2024

Jeasson F. Gonzalez Open the ORCID record for Jeasson F. Gonzalez [Opens in a new window] ,
L. Zavala Sansón Open the ORCID record for L. Zavala Sansón [Opens in a new window]  and
F. Graef Open the ORCID record for F. Graef [Opens in a new window]
Jeasson F. Gonzalez*
Affiliation:
Secretaría de Educación del Distrito Capital, Bogotá 110931, Colombia
L. Zavala Sansón
Affiliation:
Departamento de Oceanografía Física, CICESE, Ensenada 22860, México
F. Graef
Affiliation:
Departamento de Oceanografía Física, CICESE, Ensenada 22860, México
*
†Email address for correspondence: [email protected]
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Abstract

Nonlinear steady solutions of the barotropic quasi-geostrophic equation in basins, gulfs and channels on a $\beta$-plane are presented. The domains are rectangular with arbitrary aspect ratios. The two-dimensional solutions assume a linear relationship between the potential vorticity $q$ and the stream function $\psi$. The sign of the slope in the linear $q\unicode{x2013}\psi$ relationship defines two broad sets of solutions. For a positive slope, the solutions in a closed basin correspond to the inertial gyres derived by Fofonoff in 1954. The negative slope solutions consist of normal modes that can be resonant. For gulfs and channels, the conditions at the open boundaries are almost arbitrary flows entering or leaving the domain. Such conditions allow a great variety of solutions in the interior, characterised mainly by arrays of vortices with alternate signs. Several examples are presented and discussed.

JFM classification

Geophysical and Geological Flows: Quasi-geostrophic flows Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 997 , 25 October 2024 , A24
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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