Scaling baroclinic eddy fluxes: vortices and energy balance

The eddy flux of heat, generated by an imposed, unstable, uniform temperature gradient is studied using a horizontally homogeneous two-mode f-plane quasigeostrophic model. We consider the simplest model of equilibrated nonlinear baroclinic instability. The eddy flux is expressed in terms of a turbulent diffusivity, D. An overview of the dependence of D on external parameters such as bottom friction, the deformation length and the domain size is provided by numerical simulations at 72 values of the nondimensional control parameters.

A dominant feature of these simulations is the emergence of strong, axisymmetric, well-separated baroclinic vortices. The core radius of a single vortex is significantly larger than the deformation length, and there is a negative correlation between core temperature and core barotropic vorticity. That is, anti-cyclonic vortices are hot, and cyclonic vortices are cold. The thermal field is dominated by these vortices: there is little thermal signal outside the cores. The eddy mixing length is roughly the separation between vortex cores, and the motion of a single vortex is due to barotropic advection by other distant vortices. The eddy heat flux is due to the systematic migration of anti-cyclones northward and cyclones southwards. These features can be explained by scaling arguments, and an analysis of the energy balance equation. These arguments result in a relation between D and the mixing length.

All the major properties of this vortex gas are exponentially sensitive to the strength of the bottom drag. As the bottom drag decreases both the vortex cores and the vortex separation become larger. Provided that the vortex separation is significantly smaller than the domain size, then local mixing length arguments are applicable. In this local-mixing regime D grows exponentially with decreasing bottom drag.

This vortex-dominated flow differs significantly from the situation envisaged by earlier scaling theories which are based on coupled Kolmogorovian cascades. In view of the coherent structures which dominate the flow, the main assumptions of these cascade theories are implausible. Thus it is not surprising that data from the simulations show their main predictions are qualitatively unreliable.