The nonlinear evolution of two surface quasi-geostrophic vortices

Abstract

We investigate numerically the evolution of a baroclinic vortex in a two-level surface quasi-geostrophic model. The vortex is composed of two circular patches of uniform buoyancy, one located at each level. We vary the vortex radii, the magnitude of buoyancy, and the vertical distance between the two levels. We also study different radial profiles of buoyancy for each vortex. This article considers two main situations: firstly, initially columnar vortices with like-signed buoyancies. These vortices are contra-rotating, are linearly unstable and may break. Secondly, we consider initially tilted vortices with opposite-signed buoyancies, which may align vertically. Numerical experiments show that (1) identical contra-rotating vortices break into hetons when initially perturbed by low azimuthal modes; (2) unstable, vertically asymmetric, contra-rotating vortices can stabilise nonlinearly more often than vertically symmetric ones, and can form quasi-steady baroclinic tripoles; (3) co-rotating vortices can align when the two levels are close to each other vertically, and when the vortices are initially horizontally distant from each other by less than three radii; (4) for initially more distant vortices, two such vortices rotate around the plane center; and(5) in all cases, the vortex boundaries are disturbed by Rossby waves. These results compare favorably to earlier results with internal quasi-geostrophic vortices. Further modelling efforts may extend the present study to fully three-dimensional ocean dynamics.

Keywords:

• Two-level model
• surface quasi-geostrophy
• vortex stability
• Burger number
• modal analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Ecole Normale Superieure de Rennes [PhD grant to Armand Vic].