Vortex merger in surface quasi-geostrophy

Abstract

The merger of two identical surface temperature vortices is studied in the surface quasi-geostrophic model. The motivation for this study is the observation of the merger of submesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incompressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and symmetric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vortex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.

Keywords:

• Surface quasi-geostrophy
• vortex merger
• steady states
• critical distance
• shear/strain flow
• numerical model

Acknowledgements

The authors wish to express their gratitude to the two referees who brought a fruitful contribution to the paper via their analysis and their insightful suggestions. They also wish to thank the editors, Pr David Dritschel and Pr Andrew Soward, for their help and for their efficient handling of this paper.

Notes

No potential conflict of interest was reported by the authors.

1 Primitive equations are Boussinesq, hydrostatic Navier–Stokes equations on a rotating planet.

2 As mentioned above, smoothing is necessary to avoid the Gibbs’ numerical instability.

3 Note that truncation errors always result in very small defects of flow symmetry; the growth of such asymmetries only depend on the flow conditions.

Additional information

Funding

D. Ciani was supported by a PhD grant from UBO and the Brittany region.