Zonal Jets in Wide Baroclinically Unstable Regions: Persistence and Scale Selection

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  • 1 Department of Meteorology, Texas A&M University, College Station, Texas
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Abstract

Extremely persistent, equivalent barotropic zonal jets are observed in statistically steady quasigeostrophic two-layer beta-plane turbulence. Flows are forced by an imposed unstable vertical shear, horizontally uniform over domains several tens of Rossby radii wide. Damping is by surface drag, small-scale mixing, and for some runs, radiative relaxation. When dissipation is weak, zonal jets emerge with a meridional scale related to beta and the equilibrated eddy energy level as suggested by Rhines. Spinup behavior suggests a priori prediction of this level will be difficult.

The scale of energy conversion also cannot be determined a priori, and while upscale energy transfer is important, (reverse) energy cascading ranges of any significant extent do not occur. Time scales considerably longer than those simply related to model parameters are prominent. The choices of doubly periodic boundary conditions and spatially homogeneous forcing and dissipation emphasize that the low-frequency behavior is due to internal dynamics.

When the domain size is an integral multiple of the jet scale, jets evolve rather independently of each other, meandering on relatively long time scales. Jet interactions are predominantly pairwise when the implicit quantization is violated. Eddy fluxes occur in intermittent bursts asymmetric about jet axes, producing momentum flux convergences to maintain the jets against surface drag. Heat fluxes are everywhere downgradient, reaching local maxima in jet cores.

Potential vorticity homogenization is not seen in these forced-dissipative equilibria. Zonally averaged potential vorticity gradients are bounded away from zero when forcing is strong, and zero crossings occur only in the lower layer at weak forcing (when they may be anticipated from the form of the forcing). The relation between potential vorticity fluxes and their gradients is determined by details of the dissipation rather than by any general principle. As seen earlier with a “one-dimensional” model, baroclinic adjustment parameterizations are inappropriate in wide domains.

Abstract

Extremely persistent, equivalent barotropic zonal jets are observed in statistically steady quasigeostrophic two-layer beta-plane turbulence. Flows are forced by an imposed unstable vertical shear, horizontally uniform over domains several tens of Rossby radii wide. Damping is by surface drag, small-scale mixing, and for some runs, radiative relaxation. When dissipation is weak, zonal jets emerge with a meridional scale related to beta and the equilibrated eddy energy level as suggested by Rhines. Spinup behavior suggests a priori prediction of this level will be difficult.

The scale of energy conversion also cannot be determined a priori, and while upscale energy transfer is important, (reverse) energy cascading ranges of any significant extent do not occur. Time scales considerably longer than those simply related to model parameters are prominent. The choices of doubly periodic boundary conditions and spatially homogeneous forcing and dissipation emphasize that the low-frequency behavior is due to internal dynamics.

When the domain size is an integral multiple of the jet scale, jets evolve rather independently of each other, meandering on relatively long time scales. Jet interactions are predominantly pairwise when the implicit quantization is violated. Eddy fluxes occur in intermittent bursts asymmetric about jet axes, producing momentum flux convergences to maintain the jets against surface drag. Heat fluxes are everywhere downgradient, reaching local maxima in jet cores.

Potential vorticity homogenization is not seen in these forced-dissipative equilibria. Zonally averaged potential vorticity gradients are bounded away from zero when forcing is strong, and zero crossings occur only in the lower layer at weak forcing (when they may be anticipated from the form of the forcing). The relation between potential vorticity fluxes and their gradients is determined by details of the dissipation rather than by any general principle. As seen earlier with a “one-dimensional” model, baroclinic adjustment parameterizations are inappropriate in wide domains.

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