Energy exchanges between two-dimensional front and internal waves.

Fronts and near-inertial waves (NIWs) are energetic motions in the upper ocean that are thought to interact and provide a possible route for kinetic energy dissipation of mesoscale balanced flows. To date, the theoretical explanations for such interactions rely on the fronts being geostrophic, with a weak ageostrophic secondary circulation (ASC) and a small Rossby number. We develop a quasilinear model to study the interactions between NIW vertical modes and a 2D front undergoing semigeostrophic frontogenesis. In our model, frontal sharpening is divided into two stages: an exponential stage, that is characterized by a low Rossby number and is driven by geostrophic strain; and a super-exponential stage, that is characterized by an O(1) Rossby number and is driven by the convergence of the ASC. We identify a new mechanism, the convergence production, through which NIWs can efficiently extract energy from the front during the super-exponential stage. It is shown that the convergence production can dominate the known mechanism of energy extraction during the exponential stage, the deformation shear production, for a relatively strong geostrophic strain field.