Near-inertial echoes of ageostrophic instability in submesoscale filaments

Abstract: Ocean submesoscales, flows with characteristic size around 10 m - 10 km, are transitional between the larger, rotationally-constrained mesoscale and three-dimensional turbulence. In this paper we present simulations of a submesoscale ocean filament. In our case, the filament is strongly sheared in both vertical and cross-filament directions and is unstable. Instability indeed dominates the early behaviour with a fast extraction of kinetic energy from the vertically sheared thermal wind. However, the instability that emerges does not exhibit characteristics that match the perhaps expected symmetric or Kelvin-Helmholtz instabilities, and appears to be non-normal in nature. The prominence of the transient response depends on the initial noise and, for large initial noise amplitudes, saturates before SI normal modes are able to develop. The action of the instability is sufficiently rapid - with energy extraction from the mean flow emerging and peaking within the first inertial period (~ 18 hr) - that the filament does not respond in a geostrophically balanced sense. Instead, at all initial noise levels, it later exhibits vertically sheared near-inertial oscillations with higher amplitude as the initial minimum Richardson number decreases. Horizontal gradients strengthen only briefly as the fronts restratify. These unstable filaments can be generated by strong mixing events at pre-existing stable structures; we also caution against inadvertently triggering this response in idealised studies that start in a very unstable state.