Spontaneous wave generation at strongly strained density fronts

Abstract

A simple analytical model is presented describing the spontaneous generation of inertia-gravity waves at density fronts subjected to strong horizontal strain rates. The model considers fronts of arbitrary horizontal and vertical structure in a semi-infinite domain, with a single boundary at the ocean surface. Waves are generated because of the acceleration of the steady uniform strain flow around the density front, analogous to the generation of lee waves via flow over a topographic ridge. Significant wave generation only occurs for sufficiently strong strain rates α > 0.2f and sharp fronts H/L > 0.5f/N, where f is the Coriolis parameter, N is the stratification, and H and L are the height and width scales of the front, respectively. The frequencies of the generated waves are entirely determined by the strain rate. The lowest-frequency wave predicted to be generated via this mechanism has a Lagrangian frequency ω = 1.93f as measured in a reference frame moving with the background strain flow. The model is intended as a first-order description of wave generation at submesoscale (1 to 10 km wide) fronts where large strain rates are commonplace. The analytical model compares well with fully nonlinear numerical simulations of the submesoscale regime.