Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. I. Numerical Simulations of a Stratified Plane Couette Flow

Journal Article · Fri Mar 10 04:00:00 EST 2017 · Astrophysical Journal

DOI:https://doi.org/10.3847/1538-4357/837/2/133· OSTI ID:22869231

Garaud, Pascale ^[1]; Gagnier, Damien ^[2]; Verhoeven, Jan ^[3]

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1. Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 (United States)
2. Institut de Recherche en Astrophysique et Planétologie (IRAP), 14, avenue Edouard Belin, F-31400 Toulouse (France)
3. Department of Earth and Planetary Sciences, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 (United States)

Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn. In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent viscosity and the turbulent diffusivity of a passive tracer as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn, namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values (JPr){sub c} for instability, adequately accounts for the transition to turbulence in the flow, with (JPr){sub c}≃0.007. This result recovers and confirms the prior findings of Prat et al. Zahn’s model for the turbulent diffusivity and viscosity, namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfactorily match our numerical data. It fails (as expected) in the limit of large stratification where the Richardson number exceeds the aforementioned threshold for instability, but it also fails in the limit of low stratification where the turbulent eddy scale becomes limited by the computational domain size. We propose a revised model for turbulent mixing by diffusive stratified shear instabilities that properly accounts for both limits, fits our data satisfactorily, and recovers Zahn’s model in the limit of large Reynolds numbers.

• OSTI ID: 22869231
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 837; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
COMPUTERIZED SIMULATION
HYDRODYNAMICS
INSTABILITY
PRANDTL NUMBER
REYNOLDS NUMBER
STABILITY
STARS
STELLAR RADIATION
STRATIFICATION
THERMAL DIFFUSION
THERMAL DIFFUSIVITY
TURBULENCE
VISCOSITY