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Vortex Dipoles for Surface Quasigeostrophic Models

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  • 1 Simon Fraser University, Burnaby, British Columbia, Canada
  • | 2 National Center for Atmospheric Research,* Boulder, Colorado
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Abstract

A new class of exact vortex dipole solutions is derived for surface quasigeostrophic (sQG) models. The solutions extend the two-dimensional barotropic modon to fully three-dimensional, continuously stratified flow and are a simple model of localized jets on the tropopause. In addition to the basic sQG dipole, dipole structures exist for a layer of uniform potential vorticity between two rigid boundaries and for a dipole in the presence of uniform background vertical shear and horizontal potential temperature gradient. In the former case, the solution approaches the barotropic Lamb dipole in the limit of a layer that is shallow relative to the Rossby depth based on the dipole’s radius. In the latter case, dipoles that are bounded in the far field must propagate counter to the phase speed of the linear edge waves associated with the surface temperature gradient.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: David J. Muraki, Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada. Email: muraki@math.sfu.ca

Abstract

A new class of exact vortex dipole solutions is derived for surface quasigeostrophic (sQG) models. The solutions extend the two-dimensional barotropic modon to fully three-dimensional, continuously stratified flow and are a simple model of localized jets on the tropopause. In addition to the basic sQG dipole, dipole structures exist for a layer of uniform potential vorticity between two rigid boundaries and for a dipole in the presence of uniform background vertical shear and horizontal potential temperature gradient. In the former case, the solution approaches the barotropic Lamb dipole in the limit of a layer that is shallow relative to the Rossby depth based on the dipole’s radius. In the latter case, dipoles that are bounded in the far field must propagate counter to the phase speed of the linear edge waves associated with the surface temperature gradient.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: David J. Muraki, Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada. Email: muraki@math.sfu.ca

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