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 non-dimensional eddy length-scale against
a nonlinearity parameter equal to the ratio of the root-mean-square eddy velocity and
baroclinic Rossby phase speed. Two estimates of the eddy length-scale are compared: the
equivalent eddy radius inferred from the area enclosed by contours of sea-surface height,
and the ‘unsuppressed’ mixing length, based on an estimate of the eddy diffusivity with
mean flow effects removed. 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.