Enhancement in vertical fluxes at a front by mesoscale‐submesoscale coupling

Oceanic frontal instabilities are of importance for the vertical exchange of properties in the ocean. Submesoscale, O(1) Rossby number, dynamics are particularly relevant for inducing the vertical (and lateral) flux of buoyancy and tracers in the mixed layer, but how these couple with the stratified pycnocline is less clear. Observations show surface fronts often persist beneath the mixed layer. Here we use idealized, three-dimensional model simulations to show how surface fronts that extend deeper into the pycnocline invoke enhanced vertical fluxes through the coupling of submesoscale and mesoscale instabilities. We contrast simulations in which the front is restricted to the mixed layer with those in which it extends deeper. For the deeper fronts, we examine the effect of density stratification on the vertical coupling. Our results show deep fronts can dynamically couple the mixed layer and pycnocline on time scales that increase with the peak stratification beneath the mixed layer. Eddies in the interior generate skew fluxes of buoyancy and tracer oriented along isopycnals, thus providing an adiabatic pathway for the interior to interact with the mixed layer at fronts. The vertical enhancement of tracer fluxes through the mesoscale-submesoscale coupling described here is thus relevant to the vertical supply of nutrients for phytoplankton in the ocean. A further implication for wind-forced fronts is that the vertical structure of the stream function characterizing the exchange between the interior and the mixed layer exhibits significant qualitative differences compared to a linear combination of existing parameterizations of submesoscale eddies in the mixed layer and mesoscale eddies in the interior. The discrepancies are most severe within the mixed layer suggesting a potential role for Ekman-layer dynamics absent in existing submesoscale parameterizations.