On the development and stabilisation of symmetrically unstable fronts

Abstract

Submesoscale fronts, with large geostrophically balanced horizontal density gradients and Rossby and Richardson numbers of O(1), are common in the upper ocean. Here, destabilizing atmospheric forcing, can maintain a surface mixed layer with weak to vanishing stratification. This weak stratification often results in areas where the Ertel potential vorticity (PV) is of opposite sign to the Coriolis parameter, leading to regions prone to a hybrid convective–inertial perturbation known as symmetric instability (SI). Growing slantwise convection cells nearly aligned with isopycnals promote the transport of climate relevant tracers important for both the biology as well as energy transfers across scales, influencing both turbulence and the broader ocean circulation.

Submesoscale dynamics challenge traditional modeling approximations and remain unresolved in standard ocean models. Through a combination of linear theory and high-resolution idealised Large Eddy Simulations (LES), we investigate the role of (forced) symmetric instability in the potential vorticity budget. The focus is on the role of symmetric instability and ultimate restratification of the ocean column once the destabilising surface forcing has ceased. Comparisons between spin-down experiments with and without a strongly stratified thermocline below the surface mixed layer, as well as forced symmetric instability, suggest that without destabilising surface forcing, the PV flux from the interior is of minor importance. Furthermore, the main contributor to the restratification process is an SI-driven divergence of cross-frontal Reynolds stresses, which leads to a cross-frontal secondary circulation triggered by a modified thermal wind that stratifies the water column. Additionally, we show that the alternating vertical momentum fluxes associated with SI lead to frontogenesis and the formation of sharp fronts at the boundaries of the mixed layer. These non-geostrophic fronts are hot-spots for vertical potential vorticity fluxes and are where secondary Kelvin-Helmholtz instabilities (KHI) first appear. We show the complex influence of turbulence on the generation of symmetric and secondary Kelvin-Helmholtz instabilities.

This work enhances our understanding of how upper ocean fronts modulate energy transfer, with consequences for both the large- and small scale ocean dynamics as well as air-sea exchanges. The findings underscore the importance of SI in mixed layer energy dynamics and highlight implications for parameterising submesoscale processes in climate models.