Oceanic restratification forced by surface frontogenesis

Potential vorticity (PV) conservation implies a strong constraint on the time evolution of the mean density at a given depth. We show that, on an f -plane and in the absence of sources and sinks of PV, it only depends on two terms, namely the time evolution of the product between density anomaly and relative vorticity, and the vertical PV flux. This primitive-equation result, that applies at any depth, suggests that the ageostrophic dynamics induced by baroclinic eddies strongly impacts the mean oceanic stratification profile. This result is illustrated for two simple initial-value simulations of a baroclinic balanced jet. For initial situations propitious to surface frontogenesis, the simulations show a restratification over the whole water column characterized by the amplification in time of the Brunt-Väisälä frequency in the upper oceanic layers. In the absence of surface frontogenesis, such as when the jet is initialized at mid-depth of the water column, the restratification is much weaker and slower. As both simulations have similar kinetic energy and growth rate of baroclinic instability, our results clearly reveal that the restratification is driven by the surface frontogenesis in the first case, and by the vertical PV flux in the interior in the second case. Finally, we also point out that the dynamics of the interior PV is tightly related to the surface dynamics because of the total mass conservation.