| Abstract: The statistical dynamics of midocean
eddies, generated by baroclinic instability of a zonal mean flow, are
studied in the context of homogeneous stratified quasigeostrophic
tubulence. 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 represent
baroclinic eddy kinetic energy, the present results are consistent with
the observed correlation between surface eddy scales and the first
radius of deformation. |