Observed Variations in Turbulent Mixing Efficiency in the Deep Ocean

Abstract

Recent progress in direct numerical simulations (DNSs) of stratified turbulent flows has led to increasing attention to the validity of the constancy of the dissipation flux coefficient Γ in the Osborn’s eddy diffusivity model. Motivated by lack of observational estimates of Γ, particularly under weakly stratified deep-ocean conditions, this study estimates Γ using deep microstructure profiles collected in various regions of the North Pacific and Southern Oceans. It is shown that Γ is not constant but varies significantly with the Ozmidov/Thorpe scale ratio ROT in a fashion similar to that obtained by previous DNS studies. Efficient mixing events with Γ ~ O(1) and ROT ~ O(0.1) tend to be frequently observed in the deep ocean (i.e., weak stratification), while moderate mixing events with Γ ~ O(0.1) and ROT ~ O(1) tend to be observed in the upper ocean (i.e., strong stratification). The observed negative relationship between Γ and ROT is consistent with a simple scaling that can be derived from classical turbulence theories. In contrast, the observed results exhibit no definite relationships between Γ and the buoyancy Reynolds number Reb, although Reb has long been thought to be another key parameter that controls Γ.

How Variable Is Mixing Efficiency in the Abyss?

“…Wide variations in the patch‐wise mixing coefficient Γ patch were observed (Figures 1 and 2). Positive variations of Γ patch with the Thorpe/Ozmidov length scale ratio L T / L O were obtained in both data sets (Figures 1a and 1b), consistent with previous numerical/laboratory/field results (e.g., Rohr & Van Atta, 1987; Smyth et al, 2001; Mashayek et al 2017; Ijichi & Hibiya, 2018). Moreover, in the BBTRE data set, where velocity finestructure data are available, positive variations of Γ patch with the Richardson number Ri are seen (Figure 1c), consistent with previous numerical/laboratory/field results (e.g., Lozovatsky & Fernando, 2013; Rohr & Van Atta, 1987).…”

“…Moreover, in the BBTRE data set, where velocity finestructure data are available, positive variations of Γ patch with the Richardson number Ri are seen (Figure 1c), consistent with previous numerical/laboratory/field results (e.g., Lozovatsky & Fernando, 2013; Rohr & Van Atta, 1987). Interestingly, these observed variations are largely consistent with the simple theoretical scalings Γ patch ∝ ( L T / L O ) 4/3 (Ivey & Imburger 1991; Ijichi & Hibiya, 2018) and Γ patch ∝ Ri (Thompson, 1980). It is important to note that these patch‐wise estimates span a wide range of turbulence intensities, well above the molecular‐ and buoyancy‐controlled regimes: the buoyancy Reynolds number Re b >> 10 (Figures 2), indicating that they are not affected by differential diffusion (Jackson & Rehmann, 2014) or anisotropic turbulence (Yamazaki & Osborn, 1990).…”

“…It is apparent from Figure 2 that the recent SKIF (Shih et al, 2005) model of decreasing Γ patch with increasing Re b is not supported by either data set: Γ patch actually tends to increase with Re b in a moderately energetic regime with 10 2 < Re b < 10 4 . Moreover, compared with the L T / L O or Ri space, Γ patch is more broadly distributed over the Re b space, suggesting that Γ patch should not be parameterized in terms of Re b , as argued previously (e.g., Ijichi & Hibiya, 2018).…”

“…Together with Γ patch , the ratio of the Thorpe scale L T to the Ozmidov scale and the buoyancy Reynolds number were computed, where we estimated the overturn‐based buoyancy frequency and L T from high‐resolution potential temperature constructed from microtemperature data to resolve much finer turbulent overturns (for more details, see Ijichi & Hibiya, 2018). In the BBTRE data set, where velocity finestructure data are available, the gradient Richardson number was also computed, where we estimated the background velocity shear for turbulent overturns by linear fitting each observed velocity profile over the computed Thorpe length scale of L T .…”

Sensitivity of Deep Ocean Mixing to Local Internal Tide Breaking and Mixing Efficiency

“…To represent such variability, Γ has often been parameterized (e.g., see Shih et al, ; Bouffard & Boegman, ) as a nonmonotonic function of the buoyancy Reynolds number, a measure of the turbulence intensity relative to stratification and viscosity, defined as where ν is the kinematic viscosity of seawater and N 2 =−( g / ρ 0 ) ∂ z ρ is the ocean density stratification where ρ 0 is a reference density and g the gravitational acceleration. Although it is by no means settled that mixing in stratified turbulence is generically a function of Re b (see, e.g., Gregg et al, ; Ijichi & Hibiya, ; Portwood et al, ), there is also strong evidence that the important abyssal mixing process mediated by shear‐driven instabilities does indeed vary nonmonotonically with Re b (Mashayek, Caulfield, & Peltier, ). Previous studies have investigated the sensitivity of the mixing‐driven deep overturning circulation to variations in Γ (De Lavergne et al, ; Mashayek, Salehipour, et al, ) but without exploring its covariation with other parameters.…”