A physical–statistical recipe for representation of small-scale oceanic turbulent mixing in climate models

Abstract

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 regulating 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, $\varGamma _B$ , 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. Here, $\varGamma _B$ depends on both the statistical distribution of turbulent patches and the flux coefficient associated with individual patches, $\varGamma _i$ . We rely on recent parametrizations of $\varGamma _i$ and the seeming universal characteristics of statistics of turbulent patches to infer $\varGamma _B$ , 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.