The General Circulation of Two-Dimensional Turbulent Flow on a Beta Plane

H. Tennekes Department of Aerospace Engineering, The Pennsylvania State University, University Park 16802

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Abstract

It is likely that several features of the mid-latitude circulation in the earth's atmosphere wig also be observed in two-dimensional, nondivergent flow with buoyant forcing and surface friction. Properly scalled, buoyancy effects are surprisingly similar to baroclinic effects. A linear stability analysis shows that the growth rate of unstable disturbances depends on zonal wavenumber in much the same way as that of baroclinic waves, except for the absence of a high-wavenumber cutoff related to the Rossby radius of deformation. The energy conversion mechanisms in buoyancy-driven two-dimensional flow closely resemble those in the atmosphere: eddy kinetic energy is maintained primarily by conversion of eddy potential energy, the kinetic energy of the mean zonal flow is maintained primarily by a reverse energy cascade, and the flow owes its existence and dynamics to the mean temperature contrast between latitude circles. The equations studied in this paper include these for enstrophy and temperature variance; the spectral fluxes of these quantities are taken into account. The maintenance of the general circulation in two-dimensional flow is described in part by a system of flux-maintenance equations. These shed light on such issues as the magnitude of the poleward eddy heat flux in developing storms and the countergradient eddy momentum flux in middle latitudes.

Abstract

It is likely that several features of the mid-latitude circulation in the earth's atmosphere wig also be observed in two-dimensional, nondivergent flow with buoyant forcing and surface friction. Properly scalled, buoyancy effects are surprisingly similar to baroclinic effects. A linear stability analysis shows that the growth rate of unstable disturbances depends on zonal wavenumber in much the same way as that of baroclinic waves, except for the absence of a high-wavenumber cutoff related to the Rossby radius of deformation. The energy conversion mechanisms in buoyancy-driven two-dimensional flow closely resemble those in the atmosphere: eddy kinetic energy is maintained primarily by conversion of eddy potential energy, the kinetic energy of the mean zonal flow is maintained primarily by a reverse energy cascade, and the flow owes its existence and dynamics to the mean temperature contrast between latitude circles. The equations studied in this paper include these for enstrophy and temperature variance; the spectral fluxes of these quantities are taken into account. The maintenance of the general circulation in two-dimensional flow is described in part by a system of flux-maintenance equations. These shed light on such issues as the magnitude of the poleward eddy heat flux in developing storms and the countergradient eddy momentum flux in middle latitudes.

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