What Controls the Vertical Structure and Horizontal Scales of Mid-Ocean Eddies?

The plausibility of local baroclinic instability as a generation mechanism for mid-ocean mesoscale eddies is examined with a two-layer, quasi-geostrophic (QG) model forced by an imposed, horizontally homogeneous, vertically sheared mean flow and dissipated through bottom Ekman friction. We seek a possible explanation of the related facts that 1)mid-ocean eddies contain somewhat more energy in the first baroclinic mode than in the barotropic mode, and 2)mid-ocean eddies appear to have their energy concentrated in the first mode deformation radius. These are true despite the fact that mid-ocean eddies contain much more kinetic energy than do the mean flows. Hence, they may be strongly nonlinear entities, and it is known that nonlinearities in the QG equations tend to push eddies towards a state of barotropic eddies at scales much larger than the deformation radius.

Sets of numerical experiments are performed with two values of the stratification parameter H1/H2 (the ratio of model layer depths), 0.2 and 1. The first represents a thermocline-like stratification, the second a uniform stratification. A simple argument shows that the upper bound on the ratio of kinetic energies in the baroclinic to barotropic kinetic energies exceeds one, as in observations, only when the stratification is surface-trapped.

Experiments with equal Ekman damping rates in the two layers are also performed for purposes of contrast. Interpretation is aided with an inequality derived from the energy and enstrophy equations. The inequality forbids the simultaneous retention of substantial energy in the baroclinic mode and in deformation scales when Ekman friction is symmetric. However, the bottom friction experiments are not so bounded, especially when the stratification is surface-trapped. Hence, the model results point towards bottom friction and surface-trapped stratification as important factors in controlling the vertical structure and horizontal scales of mid-ocean eddies.