Two-Layer Geostrophic Dynamics. Part II: Geostrophic Turbulence

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  • 1 Lamont-Doherty Geological Observatory of Columbia Universary, Palisades, New York
  • | 2 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire
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Abstract

In Part I of this series, generalized geostrophic equations were formulated for the two-layer system on a beta plane and over a flat bottom. Here numerical experiments with these equations are carried out to study freely evolving geostrophic turbulence. In contrast with the classical quasigeostrophic analysis, the emphasis is placed on the finite amplitude of the vertical displacement (the frontal effect).

A previous study with a reduced-gravity, generalized geostrophic equation has shown that geostrophic turbulence of finite amplitude (frontal geostrophic turbulence) evolves toward a statistical equilibrium state dominated by large, coherent anticyclones. The present study reveals that, in the presence of baroclinicity, this statistical equilibrium state can only be reached if the finite-amplitude turbulent flow evolves from scales smaller or equal to the baroclinic deformation radius. Although the emerging anticyclones should be unstable according to the classical quasigeostrophic theory of baroclinic instability, they nonetheless appear to be stable within the present, generalized-geostrophic formalism. By their stability, they prevent potential energy from being released by baroclinic instability to the barotrophic flow.

Finally, similarities and differences between the evolution of two-layer geostrophic turbulence in the quasi-geostrophic regime, on one hand, and the frontal (finite-amplitude) geostrophic regime, on the other, are discussed and summarized.

Abstract

In Part I of this series, generalized geostrophic equations were formulated for the two-layer system on a beta plane and over a flat bottom. Here numerical experiments with these equations are carried out to study freely evolving geostrophic turbulence. In contrast with the classical quasigeostrophic analysis, the emphasis is placed on the finite amplitude of the vertical displacement (the frontal effect).

A previous study with a reduced-gravity, generalized geostrophic equation has shown that geostrophic turbulence of finite amplitude (frontal geostrophic turbulence) evolves toward a statistical equilibrium state dominated by large, coherent anticyclones. The present study reveals that, in the presence of baroclinicity, this statistical equilibrium state can only be reached if the finite-amplitude turbulent flow evolves from scales smaller or equal to the baroclinic deformation radius. Although the emerging anticyclones should be unstable according to the classical quasigeostrophic theory of baroclinic instability, they nonetheless appear to be stable within the present, generalized-geostrophic formalism. By their stability, they prevent potential energy from being released by baroclinic instability to the barotrophic flow.

Finally, similarities and differences between the evolution of two-layer geostrophic turbulence in the quasi-geostrophic regime, on one hand, and the frontal (finite-amplitude) geostrophic regime, on the other, are discussed and summarized.

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