Equilibration of Symmetric Instability and Inertial Oscillations at a Finite-Width Submesoscale Front

Submesoscale fronts with large lateral buoyancy gradients and O(1) Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) — a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. The growing linear SI modes eventually break down through a secondary shear instability, leading to three-dimensional turbulence and vertically mixing the geostrophic momentum. Once out of thermal wind balance, the front undergoes inertial oscillations which can drive further small-scale turbulence.

Here, we consider the problem of an initially balanced front with a horizontal buoyancy gradient of finite width and bounded by flat no-stress horizontal surfaces. We study the evolution to equilibration of this symmetrically-unstable front using a linear stability analysis and three-dimensional nonlinear numerical simulations. We find drastically different behaviour emerging at late times depending on the strength and width of the front. While weak fronts develop frontlets and excite subinertial oscillations, stronger fronts produce bore-like gravity currents that propagate along the top and bottom boundaries. Although the instantaneous turbulent dissipation rate can be much larger in these strong fronts, the turbulence is intermittent and peaks during periods of weak stratification. We explain the energetics as the front evolves towards the final adjusted state in terms of the dimensionless front strength and aspect ratio.