O cean turbulence influences the transport of heat, freshwater, dissolved gases such as CO 2 , pollutants, and other tracers. It is central to understanding ocean energetics and reducing uncertainties in global circulation and simulations from climate models. The dissipation of turbulent energy in stratified water results in irreversible diapycnal (across density surfaces) mixing. Recent work has shown that the spatial and temporal inhomogeneity in diapycnal mixing may play a critical role in a variety of climate phenomena. Hence, a quantitative understanding of the physics that drive the distribution of diapycnal mixing in the ocean interior is fundamental to understanding the ocean's role in climate.Diapycnal mixing is very difficult to accurately parameterize in numerical ocean models for two reasons. The first one is due to the discrete representation of tracer advection in directions that are not perfectly aligned with isopycnals, which can result in numerically induced mixing from truncation errors that is larger than observed diapycnal mixing (Griffies et al. 2000;Ilıcak et al. 2012). The second reason is related to the intermittency of turbulence, which is generated by complex and chaotic motions that span a large space-time range. Furthermore, this mixing is driven by a wide range of processes with distinct governing physics that create a rich global geography [see MacKinnon et al. (2013c) for a review]. The difficulty is also related to the relatively sparse direct sampling of ocean mixing, whereby sophisticated ship-based measurements are generally required to accurately characterize ocean mixing processes. Nonetheless, we have sufficient evidence from theory, process models, laboratory experiments, and field measurements to conclude that away from ocean boundaries (atmosphere, ice, or the solid ocean bottom), diapycnal mixing is largely related to the breaking of internal gravity waves, which have a complex dynamical underpinning and associated geography. The study summarizes recent advances in our understanding of internal wave-driven turbulent mixing in the ocean interior and introduces new parameterizations for global climate ocean models and their climate impacts.

Oceanic density overturns are commonly used to parameterize the dissipation rate of turbulent kinetic energy. This method assumes a linear scaling between the Thorpe length scale L T and the Ozmidov length scale L O . Historic evidence supporting L T ; L O has been shown for relatively weak shear-driven turbulence of the thermocline; however, little support for the method exists in regions of turbulence driven by the convective collapse of topographically influenced overturns that are large by open-ocean standards. This study presents a direct comparison of L T and L O , using vertical profiles of temperature and microstructure shear collected in the Luzon Strait-a site characterized by topographically influenced overturns up to O(100) m in scale. The comparison is also done for open-ocean sites in the Brazil basin and North Atlantic where overturns are generally smaller and due to different processes. A key result is that L T /L O increases with overturn size in a fashion similar to that observed in numerical studies of Kelvin-Helmholtz (K-H) instabilities for all sites but is most clear in data from the Luzon Strait. Resultant bias in parameterized dissipation is mitigated by ensemble averaging; however, a positive bias appears when instantaneous observations are depth and time integrated. For a series of profiles taken during a spring tidal period in the Luzon Strait, the integrated value is nearly an order of magnitude larger than that based on the microstructure observations. Physical arguments supporting L T ; L O are revisited, and conceptual regimes explaining the relationship between L T /L O and a nondimensional overturn size c L T are proposed. In a companion paper, Scotti obtains similar conclusions from energetics arguments and simulations.

An alternative framework for parameterizing stably stratified shear-flow turbulence is presented. Using dimensional analysis, four non-dimensional parameters of interest are identified that consider the independent effects of stratification, shear, viscosity, and scalar diffusivity. In the interest of geophysical applications, the problem is further simplified by considering only high Reynolds number flow. This leads to a two-dimensional parameter space based on a buoyancy strength parameter (i.e., an inverse Froude number) and a shear strength parameter. Consideration for the gradient Richardson number allows the space to be divided into an unforced regime, a shear-dominated regime, and a buoyancy-dominated regime. On this basis, a large database of direct numerical simulation and laboratory data from various sources is evaluated. Of particular interest is the observed length scale of overturning. Overturns are found to scale with k1/2/N in the buoyancy-dominated regime, k1/2/S in the shear-dominated regime, and k3/2/ε in the unforced regime, where k, N, S, and ε are the turbulent kinetic energy, buoyancy frequency, mean shear rate, and turbulent kinetic energy dissipation rate, respectively. Implications for estimates of diapycnal mixing in the ocean are discussed and a new parameterization for eddy diffusivity is presented.

Direct numerical simulations of stably stratified turbulence are used to compare the Thorpe overturn length scale, L T , with other length scales of the flow that can be constructed from large-scale quantities fundamental to shear-free, stratified turbulence. Quantities considered are the turbulent kinetic energy, k, its dissipation rate, , and the buoyancy frequency, N. Fundamental length scales are then the Ozmidov length scale, L O , the isotropic large scale, L k , and a kinetic energy length scale, L kN . Behavior of all three fundamental scales, relative to L T , is shown to be a function of the buoyancy strength parameter NT L , where T L = k/ is the turbulence time scale. When buoyancy effects are dominant (i.e., for NT L > 1), L T is shown to be linearly correlated with L kN and not with L O as is commonly assumed for oceanic flows. Agreement between L O and L T is only observed when the buoyancy and turbulence time scales are approximately equal (i.e., for the critical case when NT L ≈ 1). The relative lack of agreement between L T and L O in strongly stratified flows is likely due to anisotropy at the outer scales of the flow where the energy transfer rate differs from . The key finding of this work is that observable overturns in strongly stratified flows are more reflective of k than . In the context of oceanic observations, this implies that inference of k, rather than , from measurements of L T is fundamentally correct when NT L ≈ 1 and most appropriate when NT L > 1. Furthermore, we show that for NT L < 1, L T is linearly correlated with L k when mean shear is absent. C 2013 AIP Publishing LLC. [http://dx.

Estimates of turbulent mixing in geophysical settings typically depend on the efficiency at which shear‐driven turbulence mixes density across isopycnals. To date, however, no unifying parameterization of diapycnal mixing efficiency exists due to the variability of natural flows and also due to certain ambiguities that arise from descriptions based on a single parameter. Here we highlight important ambiguities of some common single‐parameter schemes in the context of a multiparameter framework that considers the independent effects of shear, buoyancy, and viscosity. Parameterizations based on the gradient Richardson number (Ri), the turbulent Froude number (FrT), and the buoyancy Reynolds number (Reb) are considered. The diagnostic ability of these parameters is examined using published data from both direct numerical simulations and field observations.