Linear Fluctuation Growth during Frontogenesis

Abstract

Abstract Near-surface, two-dimensional (2D) baroclinic frontogenesis induced by a barotropic deformation flow enhances the growth of three-dimensional (3D) fluctuations that occur on an ever smaller scale as the front progressively sharpens. The 3D fluctuation growth rate further increases with a larger deformation rate. The fluctuations grow by a combination of baroclinic and barotropic energy conversions from the 2D frontal flow, with the former dominating for most of the situations examined, ranging from small to 𝒪(1) values of the Rossby and Froude numbers and nondimensional deformation rate. Averaged 3D fluctuation buoyancy fluxes resist the 2D frontogenesis by a frontolytic tendency. They also augment the buoyancy restratification and potential-to-kinetic energy conversion tendencies of the 2D frontogenesis itself, and the 2D frontogenetic and 3D eddy-induced secondary circulations are mostly reinforcing (unlike in turbulent baroclinic jets). This shows that frontal instability coexists with, and potentially may even overcome, active frontogenesis; this conclusion is contrary to some previous studies. Frontal instability thus can augment frontogenesis in accomplishing a forward cascade of energy from oceanic mesoscale eddies into the submesoscale regime en route to finescale dissipation.