Downscale energy fluxes in scale-invariant oceanic internal wave turbulence

We analyse analytically and numerically the scale-invariant stationary solution to the internal-wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading-order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-collinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale-invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wavenumbers in both the vertical and the horizontal directions. Our results compare favourably with the finescale parametrization of ocean mixing that was proposed in Polzin et al.

Automated summary

The study analyzed the scale-invariant stationary solution to the internal-wave kinetic equation, finding that the main contributions to resonant energy transfers come from triads with extreme scale separation and quasi-collinear waves in the horizontal plane. Using the modified scale-invariant limit of the Garrett and Munk spectrum of internal waves, the magnitude of energy flux towards high wavenumbers in both vertical and horizontal directions was calculated, showing favorable comparison with finescale parametrization of ocean mixing proposed by Polzin et al.