Explaining the Baroclinic-Instability-Induced Frontogenesis and Frontolysis Using an Effective Beta Parameter

Abstract Submesoscale frontogenesis can be induced by multiple mechanisms, including the mixed layer baroclinic instability (BCI). Development of the BCI is linked to a horizontal density gradient that can induce a horizontal gradient of the potential vorticity, denoted as an effective beta parameter , where f is the Coriolis parameter, α is the isopycnal slope, and is a characteristic depth associated with the vertical stretching. It remains less explored how the BCI-induced frontogenesis is related to this beta parameter and how their relation is affected by the turbulent mixing. These are investigated here using idealized numerical simulations. The results show that both the alongfront and cross-front convergence are important. The dynamics of the cross-front convergence and the relative vorticity is further diagnosed using their evolution tendency equations. Temporal change of the cross-front convergence receives important contributions from the horizontal velocity shear that is linked to the alongfront fluctuation of the cross-front velocity, whereas changes in the relative vorticity are mainly due to horizontal advection and vortex stretching. Joint action of the cross-front convergence and the relative vorticity induces frontogenesis and frontolysis. We proposed that the fluctuation of the cross-front velocity and the resulting cross-front convergence can be explained using the effective beta parameter . Thus, and the associated nonlinearity play an important role in driving frontogenesis and frontolysis. Turbulent mixing is found to counteract the nonlinearity associated with . Overall, and the associated nonlinearity potentially can be used to distinguish the mixed layer BCI from other frontogenesis mechanisms.