Frontogenesis and Frontal Breakdown

Recent numerical simulations of oceanic flows on a fine spatial gridscale show that an energy transfer to submesoscales (O(1)km) takes place. In particular, they show that this transition commonly takes place as surface-frontogenesis is interrupted by submesoscale mechanisms that lead to submesoscale instabilities among which are secondary frontogenesis events. Motivated by these findings we ask the fundamental question of what kind of instabilities can compete with active frontogenesis.

We look at three dimentional flucutations on the two-dimensional Hoskins--Bretherton (1972) model of a strain-induced frontogenesis from an oceanic perspective. The front is straight, and a simple change of coordinates allows us to consider fluctuation-solutions that are linear combinations of cos(y) and sin(y) in the along-front y-direction. Breeding the Boussinesq equations numerically over reasonably sized time intervals allows us to identify the fastest growing frontal-fluctuationmodes. Hence, we identify the modes that effectively compete with the frontogenesis and possibly alter the progress of frontogenesis.