A unifying framework for parameterizing stably stratified shear-flow turbulence

Abstract

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.

Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part I: Assessments from Large-Scale Overturns in Oceanographic Data

“…In the weakly stratified limit, however, assumption 1 fails as APE vanishes. In this well-mixed regime, overturns are relieved of the anisotropic influence of stratification-a condition more supportive of assumption 2, as suggested by the results of Mater et al (2013) and Mater and Venayagamoorthy (2014) in what is essentially a shear-free inertia-dominated (quasi isotropic) regime. The array of classic datasets lends support to both assumptions only at the threshold between buoyancy-and inertia-dominated regimes when Ri ' Ri c and Fr…”

“…7 Regime B is populated with the weakly forced, small overturns of NATRE and BBTRE data that are occurring in the presence of stronger stratification. This regime is perhaps analogous to the buoyancy-dominated regime of Mater and Venayagamoorthy (2014), where assumption 1 may hold but assumption 2 is likely violated because of buoyancy-induced anisotropy at the outer scales that effectively truncates the inertial subrange to smaller scales. Taken together, however, weakly forced data of regimes B and C indicate a central tendency of L T ' L O in agreement with classic thermocline observations.…”

“…In other words, the turbulent Froude number defined by Fr k [ /(kN) is assumed to be O(1) (Mater et al 2013). First, consider the assumptions 1 and 2 in the case of shear-driven turbulence where the APE is sourced directly from the TKE reservoir of the turbulent motions.…”

“…That is, in the limit where the overturns are a product of the turbulence. In an investigation of homogeneous sheardriven turbulence of classic laboratory and DNS experiments, Mater and Venayagamoorthy (2014) Fig. 4), where S 5 du/dz is the mean shear in the unidirectional flows studied.…”

Turbulent Length Scales in a Fast-flowing, Weakly Stratified, Strait: Cook Strait, New Zealand

“…Wesson and Gregg (1994) set the scene for the research theme 15 surveying turbulence quantities in the exchange-dominated Straits of Gibraltar where they were able to quantify key turbulence parameters as driven both by internal shear and boundary mixing. Mater and Venayagamoorthy (2014) lay out a pictorial representation of length scales in stratified turbulence. The observed Thorpe overturning scale, LT, is a relatively measurable quantity associated with ocean structure and can be considered the energy baring scale.…”