Mixing efficiency in stably-stratified decaying turbulence

Rohr, Jim; Itsweire, E. C.; Atta, C. W. Van

doi:10.1080/03091928408248190

Cited by 42 publications

(28 citation statements)

References 18 publications

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“…Several estimations in the oceanic thermocline, lakes, or laboratory experiments (water tank) indicate 0.1<γ <0.4 (e.g. McEwan, 1983;Rohr et al, 1984;Gargett and Moum, 1995;Moum, 1996). In-situ and radar estimations in the UTLS indicate 0.06<γ <0.3 (Alisse and Sidi, 2000a;Dole et al, 2001).…”

Section: The Dissipation Rates Ratiomentioning

confidence: 99%

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Turbulent diffusivity in the free atmosphere inferred from MST radar measurements: a review

Wilson¹

2004

Ann. Geophys.

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Abstract. The actual impact on vertical transport of smallscale turbulence in the free atmosphere is still a debated issue. Numerous estimates of an eddy diffusivity exist, clearly showing a lack of consensus. MST radars were, and continue to be, very useful for studying atmospheric turbulence, as radar measurements allow one to estimate the dissipation rates of energy (kinetic and potential) associated with turbulent events. The two commonly used methods for estimating the dissipation rates, from the backscattered power and from the Doppler width, are discussed. The inference methods of a local diffusivity (local meaning here "within" the turbulent patch) by using the dissipation rates are reviewed, with some of the uncertainty causes being stressed. Climatological results of turbulence diffusivity inferred from radar measurements are reviewed and compared.As revealed by high resolution MST radar measurements, atmospheric turbulence is intermittent in space and time. Recent theoretical works suggest that the effective diffusivity of such a patchy turbulence is related to statistical parameters describing the morphology of turbulent events: filling factor, lifetime and height of the patches. It thus appears that a statistical description of the turbulent patches' characteristics is required in order to evaluate and parameterize the actual impact of small-scale turbulence on transport of energy and materials. Clearly, MST radars could be an essential tool in that matter.

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Section: The Dissipation Rates Ratiomentioning

confidence: 99%

“…A "canonical" R f =0.25 gives γ =1/3 (Lilly et al, 1974, based on Thorpe (1973) Rohr et al (1984) and Weinstock (1992). (1978) suggests γ ≈0.8.…”

Section: The Dissipation Rates Ratiomentioning

confidence: 99%

Turbulent diffusivity in the free atmosphere inferred from MST radar measurements: a review

Wilson¹

2004

Ann. Geophys.

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“…The discussion is typically framed in terms of the flux Richardson number R f and the density ratio R ϭ ‫ץ͗␣‬ z ‫ץ͗␤/͘‬ z S͘, where ␣ and ␤ are the coefficients of thermal expansion and haline contraction. For shear instability, laboratory experiments (Linden 1979;Rohr et al 1984) suggest 0.05 Յ R f Յ 0.25. In oceanic applications shear instabilities are associated with breaking internal waves and R f is found to be close to its maximum value 0.25 (Polzin 1996).…”

Section: ͑412͒mentioning

confidence: 99%

Finescale Structure of the T–S Relation in the Eastern North Atlantic

Ferrari

Polzin

2005

Journal of Physical Oceanography

105

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Distributions of temperature (T ) and salinity (S) and their relationship in the oceans are the result of a balance between T-S variability generated at the surface by air-sea fluxes and its removal by molecular dissipation. In this paper the role of different motions in setting the cascade of T-S variance to dissipation scales is quantified using data from the North Atlantic Tracer Release Experiment (NATRE). The NATRE observational programs include fine-and microscale measurements and provide a snapshot of T-S variability across a wide range of scales from basin to molecular. It is found that microscale turbulence controls the rate of thermal dissipation in the thermocline. At this level the T-S relation is established through a balance between large-scale advection by the gyre circulation and small-scale turbulence. Further down, at the level of intermediate and Mediterranean waters, mesoscale eddies are the rate-controlling process. The transition between the two regimes is related to the presence of a strong salinity gradient along density surfaces associated with the outflow of Mediterranean waters. Mesoscale eddies stir this gradient and produce a rich filamentation and salinity-compensated temperature inversions: isopycnal stirring and diapycnal mixing are both required to explain the T-S relation at depth.

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“…Note that there is another common definition Ri f = G/(G + 1) [e.g., Rohr et al, 1984;Ivey and Imberger, 1991], but (12) is used in this study because it is more convenient in developing the parameterizations. Note also that Ri f → ∞ as Sh d → 0 with this definition, because Sh d = 0 and G = 0 in unsheared stratified flows.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…[3] The effects of stratification on turbulence are often analyzed using the turbulent Froude number Fr or the gradient Richardson number Ri g in laboratory studies [e.g., Rohr et al, 1984Rohr et al, , 1988bYoon and Warhaft, 1990], Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) studies [e.g., Holt et al, 1992;Kaltenbach et al, 1994;Shih et al, 2000Shih et al, , 2005, and field studies [e.g., Peters et al, 1995;Stacey et al, 1999;Yeates, 2008]. These nondimensional numbers are defined as…”

Section: Introductionmentioning

confidence: 99%

Parameterizing individual effects of shear and stratification on mixing in stably stratified shear flows

Shimizu

2012

J. Geophys. Res.

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[1] This study proposes new parameterizations of diapycnal mixing by reanalyzing the results of previous laboratory and numerical experiments on homogeneous stably stratified shear flows. Unlike previous studies that use either the turbulent Froude number Fr or gradient Richardson number Ri g , this study parameterizes nondimensional momentum and buoyancy fluxes as functions of Fr and a turbulent shear number Sh, in order to quantify individual effects of shear and stratification. Turbulent momentum flux is found to depend linearly on Sh and to decrease monotonically with decreasing Fr. Turbulent buoyancy flux has a peak at moderate Fr. With increasing Sh, it decreases and increases at high and low Fr, respectively. The increase of Sh also cause relatively small but significant decreases of nondimensional turbulent properties, such as the nondimensional conversion rate of turbulent potential energy to background potential energy. The proposed parameterizations lie within the scatter of limited available field data. The parameterizations may be reduced to Ri g -based ones by incorporating the relationship between Ri g and turbulence intensity observed in the field. Existing stability functions for two-equation turbulent closure schemes are found to over-predict mixing efficiency at low Fr.

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Mixing efficiency in stably-stratified decaying turbulence

Cited by 42 publications

References 18 publications

Turbulent diffusivity in the free atmosphere inferred from MST radar measurements: a review

Turbulent diffusivity in the free atmosphere inferred from MST radar measurements: a review

Finescale Structure of the T–S Relation in the Eastern North Atlantic

Parameterizing individual effects of shear and stratification on mixing in stably stratified shear flows

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