Vertical Mixing and Transports through a Stratified Shear Layer

Strang, E. J.; Fernando, H. J. S.

doi:10.1175/1520-0485(2001)031<2026:vmatta>2.0.co;2

Cited by 102 publications

(109 citation statements)

References 47 publications

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“…In fact, several recent data have shown that mixing persists even after Ri = 1. These data include meteorological observations (Kondo et al 1978;Bertin et al 1997;Mahrt & Vickers 2005;Uttal et al 2002;Poulos et al 2002;Banta et al 2002), lab experiments (Strang & Fernando 2001;Rehmann & Koseff 2004;Ohya 2001), LES Zilitinkevich & Esau 2007), DNS (Stretch et al 2001), oceanic measurements (Mack & Schoeberlein 2004), and theoretical modeling (Sukoriansky et al 2005). constructed a model called "energy and flux-budget turbulence closure" that has no Ri(cr).…”

Section: Features Of the Model: No Ri(cr)mentioning

confidence: 99%

Stellar mixing

Canuto

2011

A&A

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In this paper we use the Reynolds stress models (RSM) to derive algebraic expressions for the following variables: a) heat fluxes; b) μ fluxes; and c) momentum fluxes. These relations, which are fully 3D, include: 1) stable and unstable stratification, represented by the Brunt-Väisäla frequency,; 2) double diffusion, salt-fingers, and semi-convection, represented by the density ratio R μ = ∇ μ (∇ − ∇ ad ) −1 ; 3) shear (differential rotation), represented by the mean squared shear Σ 2 or by the Richardson number, Ri = N 2 Σ −2 ; 4) radiative losses represented by a Peclet number, Pe; 5) a complete analytical solution of the 1D version of the model. In general, the model requires the solution of two differential equations for the eddy kinetic energy K and its rate of dissipation, ε. In the local and stationary cases, when production equals dissipation, the model equations are all algebraic.

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Section: Features Of the Model: No Ri(cr)mentioning

confidence: 99%

Stellar mixing

Canuto

2011

A&A

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“…Turbulence modeling provides the two dynamic equations satisfied by Kand ε (Canuto 1998;Kupka 2001). The second problem is that a large variety of independent data from laboratory to large eddy simulations (Webster 1964;Istweire & Helland 1989;Schumann & Gerz 1995;Wang et al 1996;Kosovic & Curry 2000;Strang & Fernando 2001) have shown that stratification has different effects on heat and momentum transport but Eq. (1b) is unable to account for that fact.…”

Section: The Problemmentioning

confidence: 99%

“…Large eddy simulation of a stable planetary boundary layer by Kosovic & Curry (2000) also conclude that mixing exists up to Ri t ≈ 1. A number of other cases leading to (3d) are discussed in Strang & Fernando (2001). From the turbulence modeling viewpoint, turbulence models (Canuto 1998) provide the dependence of the turbulent kinetic energy K on Ri.…”

Section: The Critical Richardson Numbermentioning

confidence: 99%

Critical Richardson numbers and gravity waves

Canuto

2002

A&A

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Abstract. In this paper we present two new results. The first concerns the proper identification of the critical Richardson number Ri(cr) above which there is no longer turbulent mixing. Thus far, all studies have assumed that:However, since Ri (cr) determines the upper limit of a laminar regime (superscript ), it has little relevance to stars where the problem is not to determine the end point of a laminar regime but the endpoint of turbulence. We show that the latter is characterized by Ri t (cr), where t stands for turbulence, and has a value four times larger than (1):We also show that use of (2) instead of (1) changes the conclusions of recent studies. Inclusion of radiative losses (characterized by the Peclet number P e) which weaken stable stratification and help turbulence, further changes (2) to (r stands for radiative):which, for P e < 1, allows turbulence to survive far longer than (2). Finally, turbulent convection generates gravity waves that propagate into the radiative region and act as an additional source of energy. This further changes Eq. (3) to (gw stands for gravity waves):where ηgw > 1. In conclusion, the successive inclusion of relevant physical processes leads to a chain of increasing values of Ri(cr):The second result concerns the dependence of the diffusivity D on Ω. We show that the commonly used expressionis not correct for the regime P e < 1 that characterizes a stably stratified regime. The proper Ω-dependence is:

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“…This formula corresponds that flux Richardson number approaches 0.2 at the Ri → ∞ limit. Strang and Fernando (2001) and Monti et al (2002) reported that Rf(Ri) does not monotonically increase but has a peak, whose value is Rf ≈ 0.4 at Ri ≈ 1. A common feature seen in the previous studies is that flux Richardson number in stable stratification has an upper limit less than unity, though its value still remains uncertain.…”

Section: Introductionmentioning

confidence: 99%

Flux Richardson Number and Turbulent Prandtl Number in a Developing Stable Boundary Layer

Kitamura

Hori²,

Yagi³

2013

Journal of the Meteorological Society of Japan

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Wind tunnel experiments and large-eddy simulations for stable stratification are performed to specify flux Richardson number Rf and turbulent Prandtl number Pr as a function of gradient Richardson number Ri. We attempted to avoid self-correlation by using independent samples for the variables commonly contained in these nondimensional numbers and confirmed the dependence of Rf and Pr on Ri for 10 −3 < Ri < 5. We found that Rf could exceed unity in a stable boundary layer under a developing stage, while the assumption of local energy balance violates for Rf > 1, which corresponds to negative production of turbulent kinetic energy. Nevertheless, the analysis of the TKE budget shows that the third-order term in the prognostic equation of TKE, which plays a role in the TKE transfer, can contribute to increase TKE despite negative TKE production. Therefore, TKE cannot be determined locally and the effects of TKE transfer must be taken into account in the region satisfying Rf > 1.

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Vertical Mixing and Transports through a Stratified Shear Layer

Cited by 102 publications

References 47 publications

Stellar mixing

Stellar mixing

Critical Richardson numbers and gravity waves

Flux Richardson Number and Turbulent Prandtl Number in a Developing Stable Boundary Layer

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