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Title: Incompressible variable-density turbulence in an external acceleration field

Abstract

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density 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 multi-scale 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 entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate$${\sim}t^{1/2}$$followed by a turbulence-dominated regime with a growth rate$${\sim}t^{3}$$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. In conclusion, the shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Connecticut, Storrs, CT (United States)
  3. 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) (NA-10)
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 0022-1120
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 variable-density turbulence in an external acceleration field. United States: N. p., 2017. Web. doi:10.1017/jfm.2017.490.
Gat, Ilana, Matheou, Georgios, Chung, Daniel, & Dimotakis, Paul E. Incompressible variable-density turbulence in an external acceleration field. United States. doi:10.1017/jfm.2017.490.
Gat, Ilana, Matheou, Georgios, Chung, Daniel, and Dimotakis, Paul E. Thu . "Incompressible variable-density turbulence in an external acceleration field". United States. doi:10.1017/jfm.2017.490. https://www.osti.gov/servlets/purl/1398345.
@article{osti_1398345,
title = {Incompressible variable-density 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 variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density 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 multi-scale 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 entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate${\sim}t^{1/2}$followed by a turbulence-dominated regime with a growth rate${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. In conclusion, the shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.},
doi = {10.1017/jfm.2017.490},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 827,
place = {United States},
year = {2017},
month = {8}
}

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Works referenced in this record:

Direct numerical simulation of buoyancy-driven turbulence in stably stratified fluid
journal, April 1993


The mixing transition in turbulent flows
journal, April 2000


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
  • DOI: 10.1063/1.868325

Numerical simulations of freely evolving turbulence in stably stratified fluids
journal, May 1989


Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence
journal, December 2009


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
  • DOI: 10.1017/S0022112000008405

Homogeneous buoyancy-generated turbulence
journal, February 1992

  • Batchelor, G. K.; Canuto, V. M.; Chasnov, J. R.
  • Journal of Fluid Mechanics, Vol. 235, Issue -1
  • DOI: 10.1017/S0022112092001149

Mixing and chemical reactions in a turbulent liquid mixing layer
journal, September 1986


The structure and dynamics of overturns in stably stratified homogeneous turbulence
journal, January 1999


Variable-density mixing in buoyancy-driven turbulence
journal, May 2008


Direct numerical simulation of stationary homogeneous stratified sheared turbulence
journal, March 2012


On the onset of high-Reynolds-number grid-generated wind tunnel turbulence
journal, August 1996


Dynamics of turbulence strongly influenced by buoyancy
journal, July 2003

  • Riley, James J.; deBruynKops, Stephen M.
  • Physics of Fluids, Vol. 15, Issue 7
  • DOI: 10.1063/1.1578077

High-Reynolds number Rayleigh–Taylor turbulence
journal, January 2009


Large-eddy simulations of turbulent mixing layers using the stretched-vortex model
journal, February 2011


Compressible Turbulent Shear Layers
journal, January 1977


Coherent structures and turbulent molecular mixing in gaseous planar shear layers
journal, July 2006


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
  • DOI: 10.1007/BF01050969

Numerical simulations of two-fluid 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
  • DOI: 10.1098/rsta.2012.0185

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
  • DOI: 10.1017/S0022112097005478

Perturbed Free Shear Layers
journal, January 1984


A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence
journal, April 1992


Spectral methods for the Navier-Stokes 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
  • DOI: 10.1016/0021-9991(91)90238-G

A method of producing a shear flow in a stratified fluid
journal, June 1968


Energy and spectral dynamics in decaying compressible turbulence
journal, March 1992

  • Kida, Shigeo; Orszag, Steven A.
  • Journal of Scientific Computing, Vol. 7, Issue 1
  • DOI: 10.1007/BF01060209

On internal gravity waves in an accelerating shear flow
journal, October 1978


Two-dimensional shear-layer entrainment
journal, November 1986

  • Dimotakis, Paul E.
  • AIAA Journal, Vol. 24, Issue 11
  • DOI: 10.2514/3.9525

Vortex dynamics in a spatially accelerating shear layer
journal, December 1998


Turbulent shear-layer mixing at high Reynolds numbers: effects of inflow conditions
journal, December 1998


Transition stages of Rayleigh–Taylor instability between miscible fluids
journal, September 2001


Direct numerical simulation of stratified homogeneous turbulent shear flows
journal, March 1989


Turbulent Mixing
journal, January 2005


Buoyancy-driven variable-density turbulence
journal, October 2007


On density effects and large structure in turbulent mixing layers
journal, July 1974


Turbulent shear layers and wakes
journal, January 2012


Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
journal, November 1882