Importance of strains in kinetic energy flux for submesoscale processes from an anisotropic perspective

Submesoscale fronts and filaments are jet-like motions, associated with cross-scale kinetic energy (KE) flux through eddy-mean flow interaction. However, the diagnostic method for KE flux in jets with a steady zonal flow axis is not suitable for submesoscale processes with arbitrary axes. Based on a high-resolution ocean model and observations, we propose a method for diagnosing KE flux via mesoscale strains and submesoscale stresses from an anisotropic perspective. Furthermore, we develop a three-dimensional anisotropic KE flux algorithm under the hydrostatic assumption, which is important for diagnosing the energy sources and distributions of submesoscale vertical instabilities. Horizontally, we find that the inverse KE cascade mainly arises from shear strain throughout the filament’s lifespan, triggering anisotropic frontogenesis and ageostrophic secondary circulations (ASCs). In ASCs, the cross-filament shear strain provides an energy source for the geostrophic shear production (GSP) and causes the forward flux through the symmetric instability. Meanwhile, the forward KE flux caused by the centrifugal instability can reach 35% of GSP which is regulated by the anisotropic eddy KE but has been neglected in previous studies. This finding effectively explains the directional dependence of strains, stresses and instabilities, broadening our understanding of energy balance and providing a foundation for improving submesoscale parameterizations.