The scales and equilibration of midocean eddies: Forced-dissipative flow

The statistical dynamics of midocean eddies. generated by baroclinic instability of a zonal mean flow. are studied in the context of homogeneous stratified quasigeostrophic turbulence. Existing theory for eddy scales and energies in fully developed turbulence is generalized and applied to a system with surface-intensified stratification and arbitrary zonal shear. The theory gives a scaling for the magnitude of the eddy potential vorticity flux, and its (momentum conserving) vertical structure. The theory is tested numerically by varying the magnitude and mode of the mean shear, the Coriolis gradient, and scale thickness of the stratification and found to be partially successful. It is found that the dynamics of energy in high (m > 1) baroclinic modes typically resembles the turbulent diffusion of a passive scalar, regardless of the stratification profile, although energy in the first mode does not. It is also found that surface-intensified stratification affects the baroclinicity of flow: as thermocline thickness is decreased, the (statistically equilibrated) baroclinic energy levels remain nearly constant but the statistically equilibrated level of barotropic eddy energy falls. Eddy statistics are found to be relatively insensitive to the magnitude of linear bottom drag in the small drag limit. The theory for the magnitude and structure of the eddy potential vorticity flux is tested against a 15-layer simulation using profiles of density and shear representative of those found in the mid North Atlantic; the theory shows good skill in representing the vertical structure of the flux, and so might serve as the basis for a parameterization of eddy fluxes in the midocean. Finally, baroclinic kinetic energy is found to concentrate near the deformation scale. To the degree that surface motions represents baroclinic eddy kinetic energy, the present results are consistent with the observed correlation between surface eddy scales and the first radius of deformation.