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Stability of a Cold Core Eddy in the Presence of Convection: Hydrostatic versus Nonhydrostatic Modeling

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  • 1 Department of Physics and Astronomy, Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands
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Abstract

Geostrophic eddies in a stratified liquid are susceptible to baroclinic instabilities. In this paper, the authors consider these instabilities when such an eddy is simultaneously cooled homogeneously from above. As a linear stability analysis shows, the developing convection modifies the background stratification, the stability boundaries, and the patterns of the dominant modes. The coupling between the effects of convection and the large-scale flow development of the eddy is studied through high-resolution numerical simulations, using both nonhydrostatic and hydrostatic models. In the latter models, several forms of convective adjustment are used to model convection. Both types of models confirm the development of the dominant modes and indicate that their nonlinear interaction leads to localized intense convection. By comparing nonhydrostatic and hydrostatic simulations of the flow development carefully, it is shown that convective adjustment may lead to erroneous small-scale variability. A simple alternative formulation of convective adjustment is able to give a substantial improvement.

* Current affiliation: Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California.

Corresponding author address: Dr. M. Jeroen Molemaker, Institution for Geophysics and Planetary Physics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90015.

Email: nmolem@atmos.ucla.edu

Abstract

Geostrophic eddies in a stratified liquid are susceptible to baroclinic instabilities. In this paper, the authors consider these instabilities when such an eddy is simultaneously cooled homogeneously from above. As a linear stability analysis shows, the developing convection modifies the background stratification, the stability boundaries, and the patterns of the dominant modes. The coupling between the effects of convection and the large-scale flow development of the eddy is studied through high-resolution numerical simulations, using both nonhydrostatic and hydrostatic models. In the latter models, several forms of convective adjustment are used to model convection. Both types of models confirm the development of the dominant modes and indicate that their nonlinear interaction leads to localized intense convection. By comparing nonhydrostatic and hydrostatic simulations of the flow development carefully, it is shown that convective adjustment may lead to erroneous small-scale variability. A simple alternative formulation of convective adjustment is able to give a substantial improvement.

* Current affiliation: Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California.

Corresponding author address: Dr. M. Jeroen Molemaker, Institution for Geophysics and Planetary Physics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90015.

Email: nmolem@atmos.ucla.edu

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