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Balanced Models and Dynamics for the Large- and Mesoscale Circulation

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  • 1 Department of Ocean Science, University of California, Santa Cruz, Santa Cruz, California
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Abstract

A balanced model that incorporates the dynamics of both the quasigeostrophic and planetary geostrophic equations is examined via numerical simulations. The model is valid for large variations in the Coriolis parameter and layer thickness, typical of dynamics at the gyre scale and larger, as well as for mesoscale dynamics in which the advection of relative vorticity cannot be neglected. For length scales much larger than the deformation radius the dominant balances in the model equations are those of the planetary geostrophic equations, whereas for synoptic scales the dynamics of the model are asymptotically close to those of the quasigeostrophic equations. The model consists of the advection of a geostrophic potential vorticity, and is is therefore conceptually simple and numerically easy to implement, requiring the solution of just one linear elliptic equation each time step. It is compared to the shallow-water equations and various other approximate models in order to assess its validity for modeling meso- and large-scale dynamics. Simulations are performed in both a periodic channel and also in a closed domain with wind stress forcing. The formulation is found to yield a substantial improvement in the qualitative nature of the circulation patterns, and in quantitative accuracy, over the planetary geostrophic and (especially) the quasigeostrophic equations, while still retaining much of the conceptual simplicity of those equations.

Corresponding author address: Dr. Geoffrey K. Vallis, Department of Ocean Science, University of California, Santa Cruz, CA 95064.

Email: vallis@cascade.ucsc.edu

Abstract

A balanced model that incorporates the dynamics of both the quasigeostrophic and planetary geostrophic equations is examined via numerical simulations. The model is valid for large variations in the Coriolis parameter and layer thickness, typical of dynamics at the gyre scale and larger, as well as for mesoscale dynamics in which the advection of relative vorticity cannot be neglected. For length scales much larger than the deformation radius the dominant balances in the model equations are those of the planetary geostrophic equations, whereas for synoptic scales the dynamics of the model are asymptotically close to those of the quasigeostrophic equations. The model consists of the advection of a geostrophic potential vorticity, and is is therefore conceptually simple and numerically easy to implement, requiring the solution of just one linear elliptic equation each time step. It is compared to the shallow-water equations and various other approximate models in order to assess its validity for modeling meso- and large-scale dynamics. Simulations are performed in both a periodic channel and also in a closed domain with wind stress forcing. The formulation is found to yield a substantial improvement in the qualitative nature of the circulation patterns, and in quantitative accuracy, over the planetary geostrophic and (especially) the quasigeostrophic equations, while still retaining much of the conceptual simplicity of those equations.

Corresponding author address: Dr. Geoffrey K. Vallis, Department of Ocean Science, University of California, Santa Cruz, CA 95064.

Email: vallis@cascade.ucsc.edu

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