Energy exchange pathways between surface and interior modes in baroclinic turbulence

In the presence of lateral gradients of buoyancy at the ocean's upper boundary, baroclinic instability preferentially injects energy into surface-intensified modes that are consistent with surface quasi-geostrophic (SQG) dynamics. Here we investigate the mechanism by which energy in such modes is exchanged with the interior, in the context of of freely-evolving simulations of quasigeostrophic turbulence. In one set of simulations, the initial condition consists of random energy in a narrow range of wavenumbers, projecting only onto surface modes with no interior potential vorticity, with and without beta. In the second set, the flow evolves from an initial flow that is unstable to an oceanic version of Charney's instability, with a uniform upper-surface buoyancy gradient and a constant interior potential vorticity gradient that is determined by both the initial shear and beta.

The energetic pathway in each case is best understood by considering its evolution through lateral scales and vertical modes. However, traditional baroclinic modes cannot efficiently capture the SQG structure, since each baroclinic mode has a vanishing vertical derivative at the surface. Here we instead use a recently-developed orthogonal modal decomposition that represents the surface-interior dynamics in a natural way, and requires only a few modes to capture nearly all the energy in our simulations. This allows for the unambiguous separation of the surface energy from the total energy. The results indicate a catalytic role for interior PV gradients, which aids the conversion of surface to interior energy. Implications for the evolution of ocean eddies will be discussed.