Incompressible variabledensity turbulence in an external acceleration field
Abstract
Dynamics and mixing of a variabledensity turbulent flow subject to an externally imposed acceleration field in the zeroMachnumber limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high and lowdensity fluid in a triply periodic domain. Density ratios in the range of$$1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$$are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multiscale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainmentratio and dominant mixedfluid composition statistics. Two mixinglayer temporal evolution regimes are identified: an initial diffusiondominated regime with a growth rate$${\sim}t^{1/2}$$followed by a turbulencedominated regime with a growth rate$${\sim}t^{3}$$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘nonmarching’) hump, corresponding to the most probable mole fraction. In conclusion, the shear layers preferentially entrain lowdensity fluid by volume at all density ratios, which is reflected in the mixedfluid composition.
 Authors:

 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Connecticut, Storrs, CT (United States)
 Univ. of Melbourne, Victoria (Australia)
 Publication Date:
 Research Org.:
 California Institute of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
 OSTI Identifier:
 1398345
 Grant/Contract Number:
 NA0002382
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 827; Journal ID: ISSN 00221120
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
Citation Formats
Gat, Ilana, Matheou, Georgios, Chung, Daniel, and Dimotakis, Paul E. Incompressible variabledensity turbulence in an external acceleration field. United States: N. p., 2017.
Web. https://doi.org/10.1017/jfm.2017.490.
Gat, Ilana, Matheou, Georgios, Chung, Daniel, & Dimotakis, Paul E. Incompressible variabledensity turbulence in an external acceleration field. United States. https://doi.org/10.1017/jfm.2017.490
Gat, Ilana, Matheou, Georgios, Chung, Daniel, and Dimotakis, Paul E. Thu .
"Incompressible variabledensity turbulence in an external acceleration field". United States. https://doi.org/10.1017/jfm.2017.490. https://www.osti.gov/servlets/purl/1398345.
@article{osti_1398345,
title = {Incompressible variabledensity turbulence in an external acceleration field},
author = {Gat, Ilana and Matheou, Georgios and Chung, Daniel and Dimotakis, Paul E.},
abstractNote = {Dynamics and mixing of a variabledensity turbulent flow subject to an externally imposed acceleration field in the zeroMachnumber limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high and lowdensity fluid in a triply periodic domain. Density ratios in the range of$1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multiscale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainmentratio and dominant mixedfluid composition statistics. Two mixinglayer temporal evolution regimes are identified: an initial diffusiondominated regime with a growth rate${\sim}t^{1/2}$followed by a turbulencedominated regime with a growth rate${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘nonmarching’) hump, corresponding to the most probable mole fraction. In conclusion, the shear layers preferentially entrain lowdensity fluid by volume at all density ratios, which is reflected in the mixedfluid composition.},
doi = {10.1017/jfm.2017.490},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 827,
place = {United States},
year = {2017},
month = {8}
}
Works referenced in this record:
Direct numerical simulation of buoyancydriven turbulence in stably stratified fluid
journal, April 1993
 Gerz, Thomas; Yamazaki, Hidekatsu
 Journal of Fluid Mechanics, Vol. 249, Issue 1
The mixing transition in turbulent flows
journal, April 2000
 Dimotakis, Paul E.
 Journal of Fluid Mechanics, Vol. 409
Direct simulation of a self‐similar turbulent mixing layer
journal, February 1994
 Rogers, Michael M.; Moser, Robert D.
 Physics of Fluids, Vol. 6, Issue 2
Numerical simulations of freely evolving turbulence in stably stratified fluids
journal, May 1989
 Métais, Olivier; Herring, Jackson R.
 Journal of Fluid Mechanics, Vol. 202
Direct numerical simulation and largeeddy simulation of stationary buoyancydriven turbulence
journal, December 2009
 Chung, D.; Pullin, D. I.
 Journal of Fluid Mechanics, Vol. 643
Scaling and parameterization of stratified homogeneous turbulent shear flow
journal, June 2000
 Shih, Lucinda H.; Koseff, Jeffrey R.; Ferziger, Joel H.
 Journal of Fluid Mechanics, Vol. 412
Homogeneous buoyancygenerated turbulence
journal, February 1992
 Batchelor, G. K.; Canuto, V. M.; Chasnov, J. R.
 Journal of Fluid Mechanics, Vol. 235, Issue 1
Mixing and chemical reactions in a turbulent liquid mixing layer
journal, September 1986
 Koochesfahani, M. M.; Dimotakis, P. E.
 Journal of Fluid Mechanics, Vol. 170
The structure and dynamics of overturns in stably stratified homogeneous turbulence
journal, January 1999
 Diamessis, Peter J.; Nomura, Keiko K.
 Journal of Fluid Mechanics, Vol. 499
Variabledensity mixing in buoyancydriven turbulence
journal, May 2008
 Livescu, D.; Ristorcelli, J. R.
 Journal of Fluid Mechanics, Vol. 605
Direct numerical simulation of stationary homogeneous stratified sheared turbulence
journal, March 2012
 Chung, D.; Matheou, G.
 Journal of Fluid Mechanics, Vol. 696
On the onset of highReynoldsnumber gridgenerated wind tunnel turbulence
journal, August 1996
 Mydlarski, L.; Warhaft, Z.
 Journal of Fluid Mechanics, Vol. 320, Issue 1
Dynamics of turbulence strongly influenced by buoyancy
journal, July 2003
 Riley, James J.; deBruynKops, Stephen M.
 Physics of Fluids, Vol. 15, Issue 7
HighReynolds number Rayleigh–Taylor turbulence
journal, January 2009
 Livescu, D.; Ristorcelli, J. R.; Gore, R. A.
 Journal of Turbulence, Vol. 10
Largeeddy simulations of turbulent mixing layers using the stretchedvortex model
journal, February 2011
 Mattner, T. W.
 Journal of Fluid Mechanics, Vol. 671
Compressible Turbulent Shear Layers
journal, January 1977
 Bradshaw, P.
 Annual Review of Fluid Mechanics, Vol. 9, Issue 1
Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics
journal, April 1998
 Staquet, C.; Godeferd, F. S.
 Journal of Fluid Mechanics, Vol. 360
Coherent structures and turbulent molecular mixing in gaseous planar shear layers
journal, July 2006
 Meyer, T. R.; Dutton, J. C.; Lucht, R. P.
 Journal of Fluid Mechanics, Vol. 558
Turbulent mixing at an accelerating interface between liquids of different density
journal, January 1979
 Anuchina, N. N.; Kucherenko, Yu. A.; Neuvazhaev, V. E.
 Fluid Dynamics, Vol. 13, Issue 6
Numerical simulations of twofluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability
journal, November 2013
 Livescu, D.
 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 2003
Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow
journal, July 1997
 Jacobitz, Frank G.; Sarkar, Sutanu; Van Atta, Charles W.
 Journal of Fluid Mechanics, Vol. 342
Perturbed Free Shear Layers
journal, January 1984
 Ho, Cm; Huerre, P.
 Annual Review of Fluid Mechanics, Vol. 16, Issue 1
A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence
journal, April 1992
 Holt, Steven E.; Koseff, Jeffrey R.; Ferziger, Joel H.
 Journal of Fluid Mechanics, Vol. 237
Spectral methods for the NavierStokes equations with one infinite and two periodic directions
journal, October 1991
 Spalart, Philippe R.; Moser, Robert D.; Rogers, Michael M.
 Journal of Computational Physics, Vol. 96, Issue 2
A method of producing a shear flow in a stratified fluid
journal, June 1968
 Thorpe, S. A.
 Journal of Fluid Mechanics, Vol. 32, Issue 4
A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
journal, May 1962
 Kolmogorov, A. N.
 Journal of Fluid Mechanics, Vol. 13, Issue 1
Energy and spectral dynamics in decaying compressible turbulence
journal, March 1992
 Kida, Shigeo; Orszag, Steven A.
 Journal of Scientific Computing, Vol. 7, Issue 1
On internal gravity waves in an accelerating shear flow
journal, October 1978
 Thorpe, S. A.
 Journal of Fluid Mechanics, Vol. 88, Issue 4
Twodimensional shearlayer entrainment
journal, November 1986
 Dimotakis, Paul E.
 AIAA Journal, Vol. 24, Issue 11
Vortex dynamics in a spatially accelerating shear layer
journal, December 1998
 Pawlak, G.; Armi, L.
 Journal of Fluid Mechanics, Vol. 376
Turbulent shearlayer mixing at high Reynolds numbers: effects of inflow conditions
journal, December 1998
 Slessor, M. D.; Bond, C. L.; Dimotakis, P. E.
 Journal of Fluid Mechanics, Vol. 376
Transition stages of Rayleigh–Taylor instability between miscible fluids
journal, September 2001
 Cook, Andrew W.; Dimotakis, Paul E.
 Journal of Fluid Mechanics, Vol. 443
Direct numerical simulation of stratified homogeneous turbulent shear flows
journal, March 1989
 Gerz, T.; Schumann, U.; Elghobashi, S. E.
 Journal of Fluid Mechanics, Vol. 200
Turbulent Mixing
journal, January 2005
 Dimotakis, Paul E.
 Annual Review of Fluid Mechanics, Vol. 37, Issue 1
Buoyancydriven variabledensity turbulence
journal, October 2007
 Livescu, D.; Ristorcelli, J. R.
 Journal of Fluid Mechanics, Vol. 591
On density effects and large structure in turbulent mixing layers
journal, July 1974
 Brown, Garry L.; Roshko, Anatol
 Journal of Fluid Mechanics, Vol. 64, Issue 4
Turbulent shear layers and wakes
journal, January 2012
 Brown, Garry L.; Roshko, Anatol
 Journal of Turbulence, Vol. 13
Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
journal, November 1882
 Rayleigh,
 Proceedings of the London Mathematical Society, Vol. s114, Issue 1