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.

References

References
1.
Godeferd
,
F. S.
, and
Cambon
,
C.
,
1994
, “
Detailed Investigation of Energy Transfers in Homogeneous Stratified Turbulence
,”
Phys. Fluids
,
6
(
6
), pp.
2084
2100
.10.1063/1.868214
2.
Livescu
,
D.
, and
Ristorcelli
,
J. R.
,
2007
, “
Buoyancy-Driven Variable-Density Turbulence
,”
J. Fluid Mech.
,
591
, pp.
43
71
.10.1017/S0022112007008270
3.
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
.10.1017/S0022112009992801
4.
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
.10.1017/S002211200100739X
5.
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
.10.1063/1.4775379
6.
Soulard
,
O.
, and
Griffond
,
J.
,
2012
, “
Inertial-Range Anisotropy in Rayleigh-Taylor Turbulence
,”
Phys. Fluids
,
24
(
2
), p.
025101
.10.1063/1.3680871
7.
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
.10.1016/j.jcp.2003.08.023
8.
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
.10.1103/PhysRevLett.88.154501
9.
Canuto
, V
.
, and
Dubovikov
,
M.
,
1996
, “
A Dynamical Model for Turbulence. I. General Formalism
,”
Phys. Fluids
,
8
, pp.
571
–586.10.1063/1.868842
10.
Sagaut
,
P.
, and
Cambon
,
C.
,
2008
,
Homogeneous Turbulence Dynamics
,
Cambridge University
,
Cambridge, UK
.
11.
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
.10.1080/14685240500055012
12.
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
.10.1063/1.3484247
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