The submesoscales of the ocean range from 0.1 km to 10 km with time-scales on the order of hours to days. In this range, inertial, rotational, and stratification effects are all important. Submesoscale fronts with large horizontal density gradients are common in the upper ocean. These fronts are associated with enhanced vertical transport and are hotspots for biological activity. Dynamics excited here dictate the exchange rate of important biogeochemical tracers such as heat or CO2 between the atmosphere and ocean interior. Submesoscale fronts in particular 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 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, the details of which strongly depend on the ratio of the horizontal buoyancy gradient to the Coriolis frequency.
Here, we consider the idealised problem of a front with uniform horizontal buoyancy gradient in thermal wind balance and bounded by flat no-stress horizontal surfaces. We study the evolution to equi- libration of this 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 relative strength of the front. While weak fronts develop frontlets and excite subinertial oscillations, stronger fronts produce bore-like gravity currents that propagate along the horizontal boundaries. Although the instantaneous turbulent dissipation rate is much larger in strong fronts, the turbulence is intermittent and peaks during periods of destratification. We describe the details of these energy pathways as the front evolves towards the final adjusted state in terms of the dimensionless front strength.