Fronts with large lateral density gradients in geostrophic and hydrostatic balance are common in the upper ocean. Such strong fronts develop through a variety of mechanisms including frontogenesis forced by mesoscale eddies, coastal upwelling, and the input of freshwater via river discharge. These fronts may be unstable to symmetric instability (SI) — a form of stratified inertial instability which occurs when the potential vorticity is of opposite sign to the Coriolis parameter. SI encourages vertical transport of biogeochemical tracers as well as of geostrophic momentum. We previously found that this momentum transport destabilises the balanced thermal wind which further enhances small-scale turbulent mixing and often leaves remnant inertial oscillations.
Here, we consider the equilibration of an initially balanced front of finite width and which is bounded by flat no-stress horizontal surfaces. We examine how the adjustment depends on the aspect ratio and strength of the front using nonlinear numerical simulations, and develop a model to predict the resultant mixing and the energy in the final equilibrated state. While fronts with Ro > 2.6 collapse to a self-similar profile dependent only on the deformation radius, we find that for small enough Ro ≲ 1, frontlets form as the front equilibrates. These frontlets increase the kinetic and potential energy of the equilibrated state and interact with the near-surface currents if the front exhibits inertial oscillations.