Research Papers: Fundamental Issues and Canonical Flows

Unstably Stratified Homogeneous Turbulence as a Tool for Turbulent Mixing Modeling

[+] Author and Article Information
J. Griffond

F-91297 Arpajon, France
e-mail: jerome.griffond@cea.fr

B. J. Gréa

F-91297 Arpajon, France
e-mail: benoit-joseph.grea@cea.fr

O. Soulard

F-91297 Arpajon, France
e-mail: olivier.soulard@cea.fr

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 22, 2013; final manuscript received October 1, 2013; published online July 9, 2014. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 136(9), 091201 (Jul 09, 2014) (6 pages) Paper No: FE-13-1040; doi: 10.1115/1.4025675 History: Received January 22, 2013; Revised October 01, 2013

In this paper, we propose a kind of buoyancy-driven flow leading to unstably stratified homogeneous (USH) turbulence. This approach is developed in the context of incompressible Navier–Stokes equations under Boussinesq approximation. We show that USH turbulence is a valuable tool for understanding and modeling turbulent mixing induced by Rayleigh-Taylor (RT) instability. It is a much simpler configuration than “RT turbulence” which is in fact inhomogeneous. Thus, it gives insights in the basic mechanisms of buoyancy-driven turbulence, namely the interplay between buoyancy production, nonlinearities and dissipation. Besides, despite their differences both types of turbulence share very similar features for the large scale characteristics as well as for the inertial range spectrum structure.

Copyright © 2014 by ASME
Topics: Turbulence
Your Session has timed out. Please sign back in to continue.


Godeferd, F. S., and Cambon, C., 1994, “Detailed Investigation of Energy Transfers in Homogeneous Stratified Turbulence,” Phys. Fluids, 6(6), pp. 2084–2100. [CrossRef]
Livescu, D., and Ristorcelli, J. R., 2007, “Buoyancy-Driven Variable-Density Turbulence,” J. Fluid Mech., 591, pp. 43–71. [CrossRef]
Chung, D., and Pullin, D., 2010, “Direct Numerical Simulation and Large-Eddy Simulation of Stationary Buoyancy-Driven Turbulence,” J. Fluid Mech., 643, pp. 279–308. [CrossRef]
Galmiche, M., and Hunt, J., 2002, “The Formation of Shear and Density Layers in Stably Stratified Turbulent Flows: Linear Processes,” J. Fluid Mech., 455, pp. 243–262. [CrossRef]
Gréa, B.-J., 2013, “The Rapid Acceleration Model and the Growth Rate of a Turbulent Mixing Zone Induced by Rayleigh-Taylor Instability,” Phys. Fluids, 25(1), p. 015118. [CrossRef]
Soulard, O., and Griffond, J., 2012, “Inertial-Range Anisotropy in Rayleigh-Taylor Turbulence,” Phys. Fluids, 24(2), p. 025101. [CrossRef]
Daru, V., and Tenaud, C., 2004, “High Order One-Step Monotonicity-Preserving Schemes for Unsteady Compressible Flow Calculations,” J. Comput. Phys., 193(2), pp. 563–594. [CrossRef]
Ishihara, T., Yoshida, K., and Kaneda, Y., 2002, “Anisotropic Velocity Correlation Spectrum at Small Scales in a Homogeneous Turbulent Shear Flow,” Phys. Rev. Lett., 88, p. 154501. [CrossRef] [PubMed]
Canuto, V., and Dubovikov, M., 1996, “A Dynamical Model for Turbulence. I. General Formalism,” Phys. Fluids, 8, pp. 571–586. [CrossRef]
Sagaut, P., and Cambon, C., 2008, Homogeneous Turbulence Dynamics, Cambridge University, Cambridge, UK.
Grégoire, O., Souffland, D., and Gauthier, S., 2005, “A Second-Order Turbulence Model for Gazeous Mixtures Induced by Richtmyer-Meshkov Instability,” J. Turbul., 6, pp. 1–20. [CrossRef]
Schilling, O., and Mueschke, N. J., 2010, “Analysis of Turbulent Transport and Mixing in Transitional Rayleigh-Taylor Unstable Flow Using Direct Numerical Simulation Data,” Phys. Fluids, 22(10), p. 105102. [CrossRef]


Grahic Jump Location
Fig. 1

Isocontours of perturbed density at ±max|ρ|/3 for USH turbulence (a) and RT turbulence (b)

Grahic Jump Location
Fig. 2

Main dimensionless turbulent parameters R, C and F with respect to the turbulence Reynolds number k2/(νɛ) for USH turbulence (a) and RT turbulence (b)

Grahic Jump Location
Fig. 3

Anisotropy spectra of longitudinal Reynolds stress with respect to wavenumber for USH turbulence (a) and RT turbulence (b); only infrared and inertial parts of the spectra is shown

Grahic Jump Location
Fig. 4

Angular spectra of longitudinal Reynolds stress with respect to the sine of the angle between gravity and wavevector for USH turbulence (a) and RT turbulence (b)

Grahic Jump Location
Fig. 5

Reynolds stress model coefficient identification from USH turbulence with respect to turbulent Reynolds number; dissipation coefficients (a), return to isotropy coefficient (b), and isotropization of the production coefficient (c)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In