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We provide a first-principles analysis of the energy fluxes in the oceanic internal wave field. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean, which is known as the finescale parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber–frequency (m–ω) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the finescale parameterization formula in functional form and in magnitude. These energy transfers are composed of a "local" and a "scale-separated" contributions; while the former is quantified numerically, the latter is dominated by the induced diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all nonzero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed "no-flux" solutions are reinstated to the status of "constant-downscale-flux" solutions. This is consequential for an understanding of energy fluxes, sources, and sinks that fits in the observational paradigm of the finescale parameterization, solving at once two long-standing paradoxes that had earned the name of "oceanic ultraviolet catastrophe." Significance Statement: The global circulation models cannot resolve the scales of the oceanic internal waves. The finescale parameterization of turbulent dissipation, a formula grounded in observations, is the standard tool by which the energy transfers due to internal waves are incorporated in the global models. Here, we provide an interpretation of this parameterization formula building on the first-principles statistical theory describing energy transfers between waves at different scales. Our result is in agreement with the finescale parameterization and points out a large contribution to the energy fluxes due to a type of wave interactions (local) usually disregarded. Moreover, the theory on which the traditional understanding of the parameterization is mainly built, a "diffusion approximation," is known to be partly in contradiction with observations. We put forward a solution to this problem, visualized by means of "streamlines" that improve the intuition of the direction of the energy cascade. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]