Resonant generation and energetics of wind-forced near-inertial motions in a submesoscale jet

Abstract:

Theory and numerical simulations are used to study the resonant generation and energetics of inertial oscillations in a unidirectional, laterally-sheared ocean current forced by oscillatory winds. The analysis applies to submesoscale geostrophic flows with Rossby numbers, Ro_g, that are of order one. In this case, the local resonant forcing frequency for inertial oscillations is modified from the Coriolis frequency $f$ to the effective Coriolis frequency F=f(1+Ro_g)^1/2. In addition, the resonant inertial velocity response is elliptical, not circular, because the oscillation periodically exchanges energy with the geostrophic flow via shear production. With damping, the energy exchange becomes permanent, but its magnitude and sign depend strongly on the angle of the oscillatory wind vector relative to the geostrophic flow. However, for an ocean forced by an isotropic distribution of wind directions, the response averaged over all wind angles results in a net extraction of energy from the geostrophic flow that scales as the wind-work on the inertial motions times Ro_g² for Ro_g <<1. For Ro_g ~ 1, this sink of kinetic energy for the circulation preferentially damps geostrophic flows with anticyclonic vorticity and thus could contribute towards shaping the positively-skewed vorticity distribution observed in the upper ocean.