Turbulent mixing induced by breaking internal waves is key to the ocean circulation and global tracer budgets. While the classic marginal shear instability of Richardson number ∼ 1/4 has been considered as potentially relevant to turbulence wave breaking, its relevance to energetic zones where tides, winds, and buoyancy gradients excite non-linearly interacting processes has been suspect. We show that shear instability is indeed relevant in the ocean interior and propose an alternative generalized marginal stability criterion, based on the ratio of Ozmidov and Thorpe turbulence scales, which not only applies to the ocean interior, but remains relevant within turbulent boundary layers. This allows for accurate quantification of the transition from downwelling to upwelling zones in a recently emerged paradigm of ocean circulation. Our results help climate models more accurately calculate the mixing-driven deep ocean circulation and fluxes of tracers in the ocean interior.

It is well established that small scale cross-density (diapycnal) turbulent mixing induced by breaking of overturns in the interior of the ocean plays a significant role in sustaining the deep ocean circulation and in regulation of tracer budgets such as those of heat, carbon and nutrients. There has been significant progress in the fluid mechanical understanding of the physics of breaking internal waves. Connection of the microphysics of such turbulence to the larger scale dynamics, however, is significantly underdeveloped. We offer a hybrid theoretical-statistical approach, informed by observations, to make such a link. By doing so, we define a bulk flux coefficient, $\Gamma_B$, which represents the partitioning of energy available to an ‘ocean box’ (such as a grid cell of a coarse resolution climate model), from winds, tides, and other sources, into mixing and dissipation. $\Gamma_B$ depends on both the statistical distribution of turbulent patches and the flux coefficient associated with individual patches, $\Gamma_i$. We rely on recent parameterizations of ~$\Gamma_i$~ and the seeming universal characteristics of statistics of turbulent patches, to infer $\Gamma_B$, which is the essential quantity for representation of turbulent diffusivity in climate models. By applying our approach to climatology and global tidal estimates, we show that on a basin scale, energetic mixing zones exhibit moderately efficient mixing that induces significant vertical density fluxes, while quiet zones (with small background turbulence levels), although highly efficient in mixing, exhibit minimal vertical fluxes. The transition between the less energetic to more energetic zones marks regions of intense upwelling and downwelling of deep waters. We suggest that such upwelling and downwelling may be stronger than previously estimated, which in turn has direct implications for the closure of the deep branch of the ocean meridional overturning circulation as well as for the associated tracer budgets.

Turbulent mixing at the sub-meter scale is an essential component of the ocean’s meridional overturning circulation and its associated global redistribution of heat, carbon, nutrients, pollutants and other tracers. Whereas direct turbulence observations in the ocean interior are limited to a modest collection of field programs, basic information such as temperature, salinity and depth is available globally. Here, we show that supervised machine learning algorithms can be trained on the existing turbulence data to develop skillful predictions of the key properties of turbulence from $T,S,Z$ and topographic data. This constitutes a promising first step toward a hybrid physics-artificial intelligence approach to parameterization of turbulent mixing in climate models.