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 K r , 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 K r 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 K r 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 3 10 25 m 2 s 21 at 1-km depth to ;1.5 3 10 24 m 2 s 21 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 408S-488N, 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 5 10 12 W), considerably less than the canonical value of ;2 TW estimated under the assumption of a uniform diffusivity of ;10 24 m 2 s 21 in the abyssal ocean.Corresponding author address: Thomas Decloedt, Marine Sciences Bldg.,

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[1] The spatial distributions of the diapycnal diffusivity predicted by two abyssal mixing schemes are compared to each other and to observational estimates based on microstructure surveys and large-scale hydrographic inversions. The parameterizations considered are the tidal mixing scheme by Jayne, St. Laurent and co-authors (JSL01) and the Roughness Diffusivity Model (RDM) by Decloedt and Luther. Comparison to microstructure surveys shows that both parameterizations are conservative in estimating the vertical extent to which bottom-intensified mixing penetrates into the stratified water column. In particular, the JSL01 exponential vertical structure function with fixed scale height decays to background values much nearer topography than observed. JSL01 and RDM yield dramatically different horizontal spatial distributions of diapycnal diffusivity, which would lead to quite different circulations in OGCMs, yet they produce similar basin-averaged diffusivity profiles. Both parameterizations are shown to yield smaller basin-mean diffusivity profiles than hydrographic inverse estimates for the major ocean basins, by factors ranging from 3 up to over an order of magnitude. The canonical 10 À4 m 2 s À1 abyssal diffusivity is reached by the parameterizations only at depths below 3 km. Power consumption by diapycnal mixing below 1 km of depth, between roughly 32 S and 48 N, for the RDM and JSL01 parameterizations is 0.40 TW & 0.28 TW, respectively. The results presented here suggest that present-day mixing parameterizations significantly underestimate abyssal mixing. In conjunction with other recently published studies, a plausible interpretation is that parameterizing the dissipation of bottom-generated internal waves is not sufficient to approximate the global spatial distribution of diapycnal mixing in the abyssal ocean.Citation: Decloedt, T., and D. S. Luther (2012), Spatially heterogeneous diapycnal mixing in the abyssal ocean: A comparison of two parameterizations to observations,

Current profiles are examined for evidence of nonlinear energy transfers from the M 2 internal tide to diurnal waves. The 6 month records, unlike shorter records, produce well-resolved velocity and shear spectra that consistently exhibit maxima at the diurnal tides O 1 and K 1 , with a minimum at the intermediate M 2 subharmonic, M 2 /2. The ratio of velocity spectral energy at M 2 /2 and M 2 is quantified, providing a needed modeling benchmark. Bispectra and bicoherences imply a negligible [ÀM 2 /2, ÀM 2 /2, ÀM 2 ] triad interaction, but possibly a significant interaction for the [ÀO 1 , ÀK 1 , ÀM 2 ] triad. Numerical simulations, however, indicate that O 1 and K 1 signals are from internal tides. Tests with synthetic data, linear tides plus random noise, reveal that bispectrum and bicoherence estimators can yield significant values, thus misleading results. Therefore, resolving the diurnal tides from M 2 /2 is essential to meaningfully assess nonlinear transfer of energy from M 2 to diurnal waves.