Mesoscale to submesoscale transition in the California current system. Part III: Energy balance and flux

This is the last of a suite of three papers about the transition that occurs in numerical simulations for an idealized equilibrium, subtropical, eastern-boundary upwelling current system similar to the California Current. The transition is mainly explained by the emergence of ubiquitous submesoscale density fronts and ageostrophic circulations about them in the weakly stratified surface boundary layer. Here the high-resolution simulations are further analyzed from the perspective of the kinetic energy (KE) spectrum shape and spectral energy fluxes in the mesoscale-to-submesoscale range in the upper ocean. For wavenumbers greater than the mesoscale energy peak, there is a submesoscale power-law regime in the spectrum with an exponent close to -2. In the KE balance an important conversion from potential to kinetic energy takes place at all wavenumbers in both mesoscale and submesoscale ranges; this conversion is the energetic counterpart of the vertical restratification flux and frontogenesis discussed in the earlier papers. A significant forward cascade of KE occurs in the submesoscale range en route to dissipation at even smaller scales. This is contrary to the inverse energy cascade of geostrophic turbulence and it is, in fact, fundamentally associated with the horizontally divergent (i.e., ageostrophic) velocity component. The submesoscale dynamical processes of frontogenesis, frontal instability, and breakdown of diagnostic force balance are all essential elements of the energy cycle of potential energy conversion and forward KE cascade.