Energy Cascades in Surface Semigeostrophic Turbulence: Implications for the Oceanic Submesoscale Flows

Abstract

Surface semigeostrophic (SSG) turbulence is examined in this study with emphasis on the effect of ageostrophy on energy cascades across the scales below the deformation radius. In our simulations, the strength of the ageostrophic component is controlled by the Rossby number $\epsilon$, varying from 0.01 to 0.2. The flows are asymmetric with preference for cold cyclonic vortices and warm anticyclonic filaments. Strong vertical motions concentrate in small-scale filaments and at the periphery of vortices where the lateral divergence becomes significant. A negative correlation between the divergence and the relative vorticity is identified using joint probability density functions. Slopes of the kinetic and potential energy spectra vary between −2.2 and −1.7. The features of the simulated flows including the asymmetry, strong vertical motion, and −2 spectral slope agree with the observations of the oceanic submesoscale flows. Analyses of spectral fluxes demonstrate an inverse kinetic energy cascade and a forward cascade of potential energy. As $\epsilon$ increases, the filaments become more numerous in the flows. They wrap around cyclones, weakening their interactions and subsequent mergers, thus suppressing the inverse cascade of kinetic energy. Ageostrophy promoting the forward potential energy cascade is important for the frontogenesis in the ocean. We characterize lateral dispersion in the SSG flows using the finite-scale Lyapunov exponents (FSLEs). They are used to identify the Lagrangian coherent structures as well as to investigate the regimes of dispersion at different scales. The results show a smooth transition from hyper-ballistic diffusion at small scales to normal diffusion at large scales.