Vertical Mixing Can Both Induce and Inhibit Submesoscale Frontogenesis

Past studies separately demonstrate that vertical boundary layer turbulence can either sharpen or weaken submesoscale fronts in the surface mixed layer.  These studies invoke competing interpretations that separately focus on the impact of either vertical momentum mixing or vertical buoyancy mixing, where the former can favor sharpening (frontogenesis) by generation of an ageostrophic secondary circulation, while the latter can weaken the front (frontolysis) via diffusion or shear dispersion.  No study comprehensively demonstrates vertical mixing induced frontogenesis and frontolysis in a common framework.  Here, we develop a unified paradigm for this problem with idealized simulations that explore how a front initially in geostrophic balance responds to a fixed vertical mixing profile.  We evolve 2D fronts with the hydrostatic, primitive equations over a range of Ekman ( Ek = 10^{-4} - 10^{-1} ) and Rossby numbers ( Ro = 0.25 - 2 ), where  Ek  quantifies the magnitude of vertical mixing and Ro quantifies the initial frontal strength.  We observe vertical  momentum  mixing induced, nonlinear frontogenesis at large  Ro  and small  Ek  and inhibition of frontogenesis via vertical  buoyancy diffusion at small Ro and large  Ek  .  Symmetric instability can dominate frontogenesis at very small  Ek ; however, the fixed mixing limits interpretation of this regime.  Simulations that suppress vertical buoyancy mixing are remarkably frontogenetic, even at large Ek , explicitly demonstrating that buoyancy mixing is frontolytic.  We identify a controlling parameter ( Ro^2 / Ek ) that quantifies the competition between cross-front buoyancy advection and vertical diffusion.  This parameter approximately maps the transition from frontolysis to frontogenesis across simulations with active buoyancy and momentum mixing.