Convective Flow in Baroclinic Vortices

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  • 1 Department of Technology. Uppsala University, Uppsala, Sweden
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Abstract

Convective flow in baroclinic vortices is studied analytically, taking viscosity ν, and thermal diffusivity κ into account. The meridional circulation depends strongly on the Prandtl number Pr = ν/κ. If Pr > 1, there is upwelling in the interior of the vortex and the vertical heal diffusion is therefore inhibited by advection. The radial flow is inward in most of the vortex, which is compensated by outward flow in a viscous boundary layer just below the surface. The authors focus on the strongly nonlinear regime, when the background stratification is much weaker than that of the vortex. It is found that the nonlinear equation governing the flow in the limit Pr ≫ 1 has a class of exact time-dependent solutions. In this class the evolution of the vertical temperature profile is determined by Burger's equation, whereas the horizontal profile is determined by the Liouville equation. Both these equations can be solved analytically.

Abstract

Convective flow in baroclinic vortices is studied analytically, taking viscosity ν, and thermal diffusivity κ into account. The meridional circulation depends strongly on the Prandtl number Pr = ν/κ. If Pr > 1, there is upwelling in the interior of the vortex and the vertical heal diffusion is therefore inhibited by advection. The radial flow is inward in most of the vortex, which is compensated by outward flow in a viscous boundary layer just below the surface. The authors focus on the strongly nonlinear regime, when the background stratification is much weaker than that of the vortex. It is found that the nonlinear equation governing the flow in the limit Pr ≫ 1 has a class of exact time-dependent solutions. In this class the evolution of the vertical temperature profile is determined by Burger's equation, whereas the horizontal profile is determined by the Liouville equation. Both these equations can be solved analytically.

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