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Abstract Small-scale turbulent mixing drives the upwelling of deep water masses in the abyssal ocean as part of the global overturning circulation¹. However, the processes leading to mixing and the pathways through which this upwelling occurs remain insufficiently understood. Recent observational and theoretical work^2–5has suggested that deep-water upwelling may occur along the ocean’s sloping seafloor; however, evidence has, so far, been indirect. Here we show vigorous near-bottom upwelling across isopycnals at a rate of the order of 100 metres per day, coupled with adiabatic exchange of near-boundary and interior fluid. These observations were made using a dye released close to the seafloor within a sloping submarine canyon, and they provide direct evidence of strong, bottom-focused diapycnal upwelling in the deep ocean. This supports previous suggestions that mixing at topographic features, such as canyons, leads to globally significant upwelling^3,6–8. The upwelling rates observed were approximately 10,000 times higher than the global average value required for approximately 30 × 10⁶m³s⁻¹of net upwelling globally⁹. 

Abstract 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 StatementThe 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: There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.