Resonant growth of inertial oscillations from lee waves in the deep ocean

Abstract

The interactions between inertial oscillations (IO) and lee waves (LW) close to the bottom of the ocean and the role of IO in energy dissipation are addressed for a range of physical parameters typical of Southern Ocean conditions. Idealized numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose. The lee waves are emitted by a uniform geostrophic flow over a sinusoidal topography for a constant buoyancy frequency at mid-latitude. We show that IO can grow by triadic resonant interactions with the LW. Two triads are dominant, which involve waves with frequency , f and , where is the intrinsic frequency of the LW and f the Coriolis frequency (assumed positive). These triads differ by the sign and value of the IO vertical wavenumber. Results from the numerical simulations show that the triad associated with the upward phase propagation of the IO is selected, consistent with oceanic observations, that a good agreement is obtained with the IO growth rate predicted theoretically and that the IO develop in a bottom layer of height less than 1000 m. A quasi-steady flow regime is eventually reached, with the IO amplitude being of the same order as the geostrophic flow speed. During this regime, depending upon the flow parameters, the IO kinetic energy is equal to 30–70% of the LW energy flux during one inertial period. This large range of values is not reflected in the turbulent kinetic energy (TKE) dissipation rate, which is comprised between 10 and 30% of the LW energy flux, whatever the IO amplitude, even if vanishingly small. Therefore, for the set of parameters we consider, the TKE dissipation rate cannot be inferred from the IO amplitude. Yet, the nonlinear interactions between the lee waves and the IO are critical in setting the energy spectrum, and similarly for the internal tide and the IO at low latitudes according to the literature. This implies that IO should be taken into account in the parameterisation of mixing in the ocean.