Baroclinic Frontal Arrest: A Sequel to Unstable Frontogenesis

In a large-scale deformation flow, lateral and vertical buoyancy gradients sharpen through baroclinic frontogenesis near the surface boundary. A thermally direct ageostrophic secondary circulation cell arises during frontogenesis to maintain geostrophic, hydrostatic (thermal wind) momentum balance for the alongfront flow. Unstable three-dimensional fluctuations can grow during frontogenesis by baroclinic instability of the alongfront shear flow that converts frontal potential energy to fluctuation energy. At finite amplitude, the fluctuations provide alongfront-averaged eddy momentum and buoyancy fluxes that arrest the frontal sharpening even while the deformation flow persists. The frontal ageostrophic secondary circulation reverses to become a thermally indirect cell in the center of the front. This allows an approximate opposition between ageostrophic advection and eddy-flux divergence in the frontal buoyancy gradient variance (i.e., frontal strength) balance equation, implying frontal equilibration. During the approximately equilibrated phase, the energy exchange rates among the deformation flow, front, and fluctuations are all reduced in comparison with a solution without eddy-flux feedback on the frontal evolution. The mean stratification is enhanced by both frontogenesis and eddy vertical buoyancy flux. The thermally indirect secondary circulation arises from eddy fluxes acting to force a departure in thermal-wind balance for the alongfront flow, overwhelming the single-cell thermally direct circulation induced by the deformation flow. The equilibrated thermal-wind imbalance in the frontal flow is appreciable, and its magnitude is set by the cross-front eddy flux of alongfront vorticity. This demonstrates an essentially inviscid, baroclinic, dynamical process for fronto-genetic arrest through frontal instability.