On a Simple Empirical Parameterization of Topography-Catalyzed Diapycnal Mixing in the Abyssal Ocean

Abstract

The global spatial distribution of the turbulent diapycnal diffusivity in the abyssal ocean is reexamined in light of the growing body of microstructure data revealing bottom-intensified turbulent mixing in regions of rough topography. A direct and nontrivial implication of the observed intensification is that the diapycnal diffusivity Kρ, is depth dependent and patchily distributed horizontally across the world’s oceans. Theoretical and observational studies show that bottom-intensified mixing is dependent upon a variety of energy sources and processes whose contributions to mixing are sufficiently complex that their physical parameterization is premature; only rudimentary parameterizations of tidally induced mixing have been attempted, although the tides likely provide no more than half of the mechanical energy available for diapycnal mixing in the abyssal ocean. Here, an empirical (and still rudimentary) parameterization of the spatially variable mean diffusivity Kρ based on a large collection of microstructure data from several oceanic regions, is provided. The parameterization, called the roughness diffusivity model (RDM), depends only on seafloor roughness and height above bottom and has the advantage of tacitly including a broad range of mixing processes catalyzed by the roughness or acuteness of the bottom topography. The study focuses in particular on the vertical structure of Kρ and shows that exponential decay, prominent in current diapycnal mixing parameterizations, does not provide an adequate representation of the mean vertical profile. Instead, an inverse square law decay with a scale height and maximum near-boundary value depending on topographic roughness is shown to provide a more realistic vertical structure. Resulting basin-averaged diffusivities based on the RDM, which increase from ∼3 × 10−5 m2 s−1 at 1-km depth to ∼1.5 × 10−4 m2 s−1 at 4 km, are roughly consistent with spatial averages derived from hydrographic data inversions, supporting the contention that strong, localized mixing plays a major role in maintaining the observed abyssal stratification. The power required to sustain the stratification in the abyssal ocean (defined as 40°S–48°N, 1–4-km depth) is shown to be sensitive to the spatial distribution of the mixing. The power consumption in this domain, given the parameterized bottom-intensified and horizontally heterogeneous diffusivity structure in the RDM, is estimated as approximately 0.37 TW (TW = 1012 W), considerably less than the canonical value of ∼2 TW estimated under the assumption of a uniform diffusivity of ∼10−4 m2 s−1 in the abyssal ocean.