A regime diagram for ocean geostrophic turbulence

A two-dimensional regime diagram for geostrophic turbulence in the ocean is constructed by plotting observation- based estimates of the nondimensional eddy radius and unsuppressed mixing length against a nonlinearity parameter equal to the ratio of the root-mean square eddy velocity and baroclinic Rossby phase speed. This regime diagram is then interpreted in terms of pertinent regime transition lines which refer to boundaries along which there is change in dynamical behaviour due to the dominance of different physical processes to either side of the transition.

For weak nonlinearity, as found in the tropics, the mixing length mostly corresponds to the stability threshold for baroclinic instability whereas the eddy radius corresponds to the Rhines scale; it is suggested that this mismatch is indicative of the inverse energy cascade that occurs at low latitudes in the ocean and the zonal elongation of eddies. At larger values of nonlinearity, as found at mid- and high-latitudes, the eddy length scales are much shorter than the stability threshold, within a factor of 2.5 of the Rossby deformation radius.

Finally implications for the construction of parameterizations of geostrophic eddies will be discussed, specifically for mixing length arguments which are used to express the eddy diffusivity as proportional to an eddy velocity multiplied by an eddy length scale.