Mean potential energy change in stratified grid turbulence

Rehmann, Chris R.; Koseff, Jeffrey R.

doi:10.1016/j.dynatmoce.2003.09.001

Cited by 59 publications

(47 citation statements)

References 40 publications

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“…Stretch et al (2010). However, the equilibrium theory does not account for layering which is often observed in the strongly stratified regime Ri ≫ 1 (Rehmann & Koseff 2004). In any case, the statistical mechanics prediction that mixing efficiency depends strongly on the global shape of the background buoyancy profile, and not only on the local buoyancy gradient is consistent with observations by Holford & Linden (1999).…”

Section: Comparison With Previous Studies Of the Efficiency Of Mixingsupporting

confidence: 75%

A statistical mechanics approach to mixing in stratified fluids

2016

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Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in these processes renders extremely difficult a deterministic approach to the problem. Here we present a statistical mechanics approach yielding a prediction for a cumulative, global mixing efficiency as a function of a global Richardson number and the background buoyancy profile. Assuming random evolution through turbulent stirring, the theory predicts that the inviscid, adiabatic dynamics is attracted irreversibly towards an equilibrium state characterised by a smooth, stable buoyancy profile at a coarse-grained level, upon which are fine-scale fluctuations of velocity and buoyancy. The convergence towards a coarse-grained buoyancy profile different from the initial one corresponds to an irreversible increase of potential energy, and the efficiency of mixing is quantified as the ratio of this potential energy increase to the total energy injected into the system. The remaining part of the energy is literally lost into small-scale fluctuations. We show that for sufficiently large Richardson number, there is equipartition between potential and kinetic energy, provided that the background buoyancy profile is strictly monotonic. This yields a mixing efficiency of 0.25, which provides statistical mechanics support for previous predictions based on phenomenological kinematics arguments. In the general case, the cumulative, global mixing efficiency predicted by the equilibrium theory can be computed using an algorithm based on a maximum entropy production principle. It is shown in particular that the variation of mixing efficiency with the Richardson number strongly depends on the background buoyancy profile. This approach could be useful to the understanding of mixing in stratified turbulence in the limit of large Reynolds and Péclet numbers.

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Section: Comparison With Previous Studies Of the Efficiency Of Mixingsupporting

confidence: 75%

A statistical mechanics approach to mixing in stratified fluids

2016

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“…This is identical to the functional dependence (5.3) shown in figure 6b based on our atmospheric dataset for much larger buoyancy Reynolds numbers, Re b > 10 3 , and therefore the dimensionless constant ξ is different. Results of several laboratory experiments [70][71][72] compiled in Shih et al [25], together with DNS data, suggest that R m ∼ Re 1/3 b (in our notation) when Re b increases from 10 2 to 10 5 . Note that the diffusivity in the laboratory experiments of Barry et al [70] with grid-generated turbulence was calculated using the change of system's background potential energy before and after mixing events, and hence is an integral measure of different turbulent regimes.…”

Section: Dependence Of Mixing Reynolds Numbers R Mχ and R Mf On Rimentioning

confidence: 99%

Mixing efficiency in natural flows

Lozovatsky

Fernando

2013

Phil. Trans. R. Soc. A.

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It is argued that the mixing efficiency of naturally occurring stratified shear flows, γ = Rf /(1− Rf ), where Rf is the flux Richardson number, is dependent on at least two governing parameters: the gradient Richardson number Ri and the buoyancy Reynolds number Re b = ε / vN 2 . It is found that, in the range approximately 0.03< Ri <0.4, which spans 10 4 < Re b <10 6 , the mixing efficiency obtained via direct measurements of fluxes and property gradients in the stable atmospheric boundary layer and homogeneous/stationary balance equations of turbulent kinetic energy (TKE) is nominally similar to that evaluated using the scalar balance equations. Outside these Ri and Re b ranges, the commonly used flux-estimation methodology based on homogeneity and stationarity of TKE equations breaks down (e.g. buoyancy effects are unimportant, energy flux divergence is significant or flow is non-stationary). In a wide range, 0.002< Ri <1, the mixing efficiency increases with Ri , but decreases with Re b . When Ri is in the proximity of Ri cr ∼0.1–0.25, γ can be considered a constant γ ≈0.16–0.2. The results shed light on the wide variability of γ noted in previous studies.

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“…Osborn (1980) suggested that a critical value of G 5 0.2 can be used to represent turbulence which persists in a steady-state flow, among other qualifications. Direct measurements of K r in laboratory experiments and estimates from numerical simulations imply that mixing efficiency is not a constant but that it can vary with stratification (Barrett and Atta 1991;Rehmann and Koseff 2004); the age of a turbulent patch (Smyth et al 2001); and buoyancy Reynolds number, Re b 5 «/nN 2 , which is also known as turbulence intensity (Barry et al 2001;Shih et al 2005). Mixing efficiency can also be represented by the flux Richardson number R f , which was defined by Ivey and Imberger (1991) as…”

Section: B the Efficiency Of Turbulent Mixingmentioning

confidence: 99%

The Modification of Bottom Boundary Layer Turbulence and Mixing by Internal Waves Shoaling on a Barrier Reef

Davis

Monismith

2011

Journal of Physical Oceanography

117

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Results are presented from an observational study of stratified, turbulent flow in the bottom boundary layer on the outer southeast Florida shelf. Measurements of momentum and heat fluxes were made using an array of acoustic Doppler velocimeters and fast-response temperature sensors in the bottom 3 m over a rough reef slope. Direct estimates of flux Richardson number R f confirm previous laboratory, numerical, and observational work, which find mixing efficiency not to be a constant but rather to vary with Fr t , Re b , and Ri g . These results depart from previous observations in that the highest levels of mixing efficiency occur for Fr t , 1, suggesting that efficient mixing can also happen in regions of buoyancy-controlled turbulence. Generally, the authors find that turbulence in the reef bottom boundary layer is highly variable in time and modified by nearbed flow, shear, and stratification driven by shoaling internal waves.

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Mean potential energy change in stratified grid turbulence

Cited by 59 publications

References 40 publications

A statistical mechanics approach to mixing in stratified fluids

A statistical mechanics approach to mixing in stratified fluids

Mixing efficiency in natural flows

The Modification of Bottom Boundary Layer Turbulence and Mixing by Internal Waves Shoaling on a Barrier Reef

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