Vertical Mixing Can Both Induce and Inhibit Submesoscale Frontogenesis

Past studies separately demonstrate that vertical boundary layer turbulence can either sharpen or weaken sub-mesoscale 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 5 10²⁴–10²¹) and Rossby (Ro 5 0.25–2) numbers, 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 demon-strating that buoyancy mixing is frontolytic. Application of two scalings to quantify the competition between cross-front buoyancy advection and vertical diffusion identifies practically equivalent controlling parameters (Ro²/Ek, Ro/Ek^1/2); these ratios approximately map regime transitions across simulations with equal vertical eddy viscosity and diffusivity. SIGNIFICANCE STATEMENT: This study reconciles competing views on how turbulent vertical mixing on scales of 0.01–1 m controls the sharpening or weakening of upper-ocean fronts characterized by horizontal changes in density and velocity over scales of 100 m–1 km. This sharpening or weakening modulates frontal circulation that acts to bring heat upward. Given the pervasiveness of such fronts, these local dynamics influence upper-ocean heat content globally. Utilizing simulations, we identify a measurable parameter that predicts frontal sharpening or weakening via vertical mixing. This new dynamical framework can better inform the necessary parameterization of these fronts in global climate models. However, future work should interrogate the validity of our simplified model, which unrealistically assumes that the vertical mixing does not evolve.