The Latitudinal Dependence of the Oceanic Barotropic Eddy Kinetic Energy and Macro-Turbulence Energy Transport

Geostrophic turbulence theory predicted already a few decades ago an inverse energy cascade in the barotropic mode, yet so far there has been no clear evidence for it. In this study, the latitudinal behavior of the oceanic barotropic energy balance and macroturbulent scales is studied using the high-resolution ECCO2 state estimate. We show that a barotropic inverse energy cascade occurs at high latitudes, as eddy-eddy interactions spread the injection of kinetic energy from the baroclinic to the barotropic mode, both upscale and downscale. At these latitudes, a classic 2D turbulence energy spectrum appears, which follows both the -5/3 and -3 slopes, at large and small scales, respectively. The importance of high latitudes in capturing the inverse energy cascade resides in the fact that the ratio of the Rossby deformation radius and the Rhines scale (QG supercriticality) plays an important role in determining the turbulent behavior of the flow. The dependence on these macro-turbulence scale is further analyzed using idealized atmospheric GCM simulations where the eddy length scales are systematically varied. This allows demonstrating that an inverse energy cascade occurs through eddy-eddy interactions at high latitudes where the Rhines scale, which coincides with the jet and the energy-containing scales, is larger than the Rossby deformation radius. The barotropic eddy kinetic energy spectrum follows a -5/3 slope between the Rossby deformation radius and the Rhines scale. Using the ECCO2 data we analyze the effect of these macroturbulent scales on barotropic inverse energy cascade processes in the ocean.