Gravity-Wave Emission from Lee-Wave Critical Layers and Energy Budgets

Direct measurements of dissipation rates in the Southern Ocean unveiled a deficit of lee-wave dissipation compared to lee-wave generation (Brearley et al. 2013; Sheen et al. 2013; Waterman et al. 2013, 2014; Cusack et al. 2017, 2020), which is described as “suppression of turbulence” in Waterman et al. (2014). One possible explanation is the generation of freely propagating internal gravity waves (free waves with Eulerian frequency 𝜔_𝐸 ≠ 0) that can radiate outside of the lee-wave critical layer and dissipate remotely. In a numerical simulation of lee waves generated by a localized, stable geostrophic current over sinusoidal topography, free waves are observed to emanate from the lee-wave critical layer. The escaped fraction of free-wave energy (the fraction that tunnels through the lee-wave critical layer and reaches the upper ocean) is 5%, while the majority remains trapped. This excludes remote dissipation by free waves as an explanation for the observed “suppression of turbulence”. Energy budget calculations show that ~50% of the bottom-generated lee-wave radiation is reabsorbed into the geostrophic current in vertical mean shear, ~10% is transferred to free waves as an indirect route to dissipation, and ~40% is lost through nonlinear wave-wave interactions leading to the increase of background potential energy. The total dissipative fraction (dissipation of lee waves plus indirect dissipation as free waves) is consistent with predictions by wave action conservation, regardless of the selected eddy viscosity and diffusivity. This study emphasizes wave-mean and wave-wave interactions in the ocean and will shed light on the choice of turbulent parameterization schemes for numerical modelers.