Dynamics and parameterization of stably stratified turbulence: implications for estimates of mixing in geophysical flows - Mater, Benjamin D., author; Venayagamoorthy, Subhas K., advisor; Bledsoe, Brian P., committee member; Dasi, Lakshmi P., committee member; Julien, Pierre Y., committee member (Colorado State University. Libraries, 2014)
This research focuses on the relationship between the observed length scales of overturns in stably-stratified shear-flow turbulence and the fundamental length scales constructed from dimensional analysis of basic physical quantities. In geophysical flows such as the ocean, overturns are relatively easy to observe while the basic quantities are not. As such, overturns provide a means of inferring basic quantities if the relationship between the observed and fundamental scales are known. In turn, inferred values of the basic quantities, namely the the turbulent kinetic energy k, and the dissipation rate of turbulent kinetic energy ϵ, can be used to estimate diapycnal diffusivity (i.e. turbulent mixing). Most commonly, the observed Thorpe length scale, LT, is assumed to scale linearly with the fundamental Ozmidov scale, LO =(ϵ/N3)1/2, so that inferred values of ϵ can be obtained and used to estimate mixing from the Osborn formulation for diapycnal diffusivity. A major goal of this research is to re-examine this and other possible scalings using dimensional analysis, direct numerical simulation (DNS), laboratory data, and field observations. The preliminary chapters constitute a fresh approach at dimensional analysis that presents the fundamental length scales, time scales, and dimensionless parameters relevant to the problem. The relationship between LT and the fundamental length scales is then examined for the simple case of homogeneously stratified turbulence (without shear) using DNS. A key finding is that the common practice of inferring ϵ from LT ~ LO, is valid at the transition between a buoyancy-dominated regime and an inertia-dominated regime where the time scale of the buoyancy oscillations, N-1, roughly matches that of the inertial motions, TL = k/ϵ. Regime definition is made possible using a non-dimensional buoyancy strength parameter NTL = Nk/ϵ. Next, the problem is generalized to consider mean shear, and thus, a shear strength parameter, STL = Sk/ϵ, and the gradient Richardson number, Ri = N2/S2, are considered along with NTL to define three regimes available to high Reynolds number stratified shear-flow turbulence: a buoyancy-dominated regime (NTL ≳ 1.7, Ri ≳ 0.25), a shear-dominated regime (STL ≳ 3.3, Ri ≲ 0.25), and an inertia-dominated regime (NTL ≲ 1.7, STL ≲ 3.3). The regimes constitute a multi-dimensional parameter space which elucidates the independent influences that shear and stratification have on the turbulence. Using a large database of DNS and laboratory results, overturns are shown to have unique scalings in the various regimes. Specifically, LT ~ k1/2N-1, LT ~ k1/2S-1, and LT ~ k3/2ϵ-1 in the buoyancy-, shear-, and inertia-dominated regimes, respectively. LT ~ LO is found only for the case of NTL = O(1) and STL ≲ 3.3, or for NTL = O(100), STL ≈ 3.3 and Ri ≈ 0.25 when shear is present. In all three regimes, LT is found to generally indicate k rather than ϵ. An alternative parameterization of turbulent diffusivity is developed based on inferred values of k with a practical eye toward field applications. When tested with DNS and laboratory data, the new model is shown to be more accurate than estimates based on inferred values of ϵ. The multi-parameter framework is broadened with consideration for the turbulent Reynolds number, ReL, thus allowing for an evaluation of existing parameterizations of diapycnal mixing efficiency, R*f. Select DNS and laboratory data sets are used in the analysis. A key finding is that descriptions of R*f based on a single-parameter are generally insufficient. It is found that Ri is an accurate parameter in the shear-dominated regime but fails in the inertia-dominated regime where turbulence is generated by external forcing (rather than mean shear). In contrast, the turbulent Froude number, FrT = (LO/LT)2/3, is an accurate parameter in the inertia-dominated regime but loses accuracy in the shear-dominated regime. Neither Ri or FrT sufficiently describe R*f in the buoyancy-dominated regime where additional consideration for ReL is needed. Another key finding is that the popular buoyancy Reynolds number, Reb = ReL(NTL)-2, is a particularly misleading parameter for describing R*f because it fails to distinguish between (i) a low-Reynolds number, weakly stratified regime of low efficiency (low ReL, low NTL, low R*f) typical of DNS flows and (ii) a high-Reynolds number, strongly stratified regime of high efficiency (high ReL, high NTL, high R*f) typical of geophysical flows. Finally, oceanic observations from Luzon Strait and the Brazil Basin are featured to examine the relationship between LT and LO in geophysical flows where turbulence is driven by overturns that are very large by open ocean standards. LT is found to increase with respect to LO as a function of the normalized overturn size LT = LTN1/2ν-1/2. When large overturns are present, dissipation rates inferred from LT ~ LO are generally larger than measured values on average. The overestimation is quantified over a spring tidal period at Luzon Strait where depth- and time-integration of inferred and measured values show that inferred energy dissipation is four times too large.
Keywords: diapycnal mixing; ocean turbulence; parameterization; scaling laws; stratified turbulence; turbulent flows