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. SI has linear eigenmodes which are capable of transporting buoyancy and geostrophic momentum. The unstable SI modes eventually break down through a secondary shear instability, leading to three-dimensional turbulence which further modifies the geostrophic momentum. An initially balanced front that is unstable to SI will evolve due to the momentum and buoyancy transport associated with SI and 3D turbulence.
Here, we consider an idealised problem with a front of finite width bounded by flat no-stress horizontal surfaces. The front is initially in thermal wind balance but there is no initial vertical stratification and the flow is unstable to SI. We study the evolution of the unstable front using a linear stability analysis and nonlinear numerical simulations. We find that the aspect ratio of the front and the ratio of the maximum horizontal buoyancy gradient to the Coriolis frequency are important parameters and influence the evolution of the front. Interesting behaviour emerges, particularly for fronts with large Rossby numbers. For example, fronts with relatively large horizontal density gradients develop bore-like gravity currents that propagate along the top and bottom boundaries. We then describe the energetics evolving towards the final adjusted state in terms of the dimensionless parameters of the system and understand these results in the context of the primary and secondary linear instability.