Skip to main content
×
Home
    • Aa
    • Aa

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

  • C. D. Tomkins (a1), B. J. Balakumar (a1), G. Orlicz (a1), K. P. Prestridge (a1) and J. R. Ristorcelli (a1)...
Abstract
Abstract

Turbulent mixing in a Richtmyer–Meshkov unstable light–heavy–light (air–${\mathrm{SF} }_{6} $–air) fluid layer subjected to a shock (Mach 1.20) and a reshock (Mach 1.14) is investigated using ensemble statistics obtained from simultaneous velocity–density measurements. The mixing is driven by an unstable array of initially symmetric vortices that induce rapid material mixing and create smaller-scale vortices. After reshock the flow appears to transition to a turbulent (likely three-dimensional) state, at which time our planar measurements are used to probe the developing flow field. The density self-correlation $b= - \langle \rho v\rangle $ (where $\rho $ and $v$ are the fluctuating density and specific volume, respectively) and terms in its evolution equation are directly measured experimentally for the first time. Amongst other things, it is found that production terms in the $b$ equation are balanced by the dissipation terms, suggesting a form of equilibrium in $b$. Simultaneous velocity measurements are used to probe the state of the incipient turbulence. A length-scale analysis suggests that an inertial range is beginning to form, consistent with the onset of a mixing transition. The developing turbulence is observed to reduce non-Boussinesq effects in the flow, which are found to be small over much of the layer after reshock. Second-order two-point structure functions of the density field exhibit a power-law behaviour with a steeper exponent than the standard $2/ 3$ power found in canonical turbulence. The absence of a significant $2/ 3$ region is observed to be consistent with the state of the flow, and the emergence of the steeper power-law region is discussed.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence
      Available formats
      ×
Copyright
This is a work of the U.S. Government and is not subject to copyright protection in the United States.
Corresponding author
Email address for correspondence: ctomkins@lanl.gov
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. Antonia , Y. Zhu & J. Kim 1993 On the measurement of lateral velocity derivatives in turbulent flows. Exp. Fluids 15, 6569.

W. D. Arnett , J. N. Bahcall , R. P. Kirshner & S. E. Woosley 1987 Supernova 1987A. Annu. Rev. Astron. Astrophys. 27, 629700.

B. J. Balakumar , G. C. Orlicz , C. D. Tomkins & K. P. Prestridge 2008 Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock. Phys. Fluids 20 (12), 124103.

A. Banerjee , R. Gore & M. Andrews 2010a Development and validation of a turbulent mix model for variable-density and compressible flows. Phys. Rev. E 82, 046309.

P. Chassaing , R. A. Antonia , F. Anselmet , L. Joly & S. Sarkar 2002 Variable Density Fluid Turbulence, Fluid Mechanics and its Applications, vol. 69, Kluwer.


P. E. Dimotakis 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329356.

O. Gregoire , D. Souffland & S. Gauthier 2005 A second-order turbulence model for gaseous mixtures induced by Richtmyer–Meshkov instability. J. Turbul. 6, N29.


B. E. Launder 1989 Second-moment closure: Present ... and future? Intl J. Heat Fluid Flow 10 (4), 282300.

D. Livescu & J. R. Ristorcelli 2008 Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech. 605, 145180.

D. Livescu & J. R. Ristorcelli 2009 Mixing asymmetry in variable density turbulence. Adv. Turbul. XII 132 (1), 545548.

D. Livescu , J. R. Ristorcelli , R. A. Gore , S. H. Dean , W. H. Cabot & A. W. Cook 2009 High-Reynolds number Rayleigh–Taylor turbulence. J. Turbul. 10 (13), 132.

J. T. Moran-Lopez & O. Schilling 2013 Multicomponent Reynolds-averaged Navier–Stokes simulations of reshocked Richtmyer–Meshkov instability-induced mixing. High Energy Density Phys. 9, 112121.

P. M. Rightley , P. Vorobieff & R. F. Benjamin 1997 Evolution of a shock-accelerated thin fluid layer. Phys. Fluids 9 (6), 17701782.

H. F. Robey , Y. Zhou , A. C. Buckingham , P. Keiter , B. A. Remington & R. P. Drake 2003 The time scale for the transition to turbulence in a high Reynolds number, accelerated flow. Phys. Plasmas 10 (3), 614622.

J. Schwarzkopf , D. Livescu , R. Gore , R. Rauenzahn & J. R. Ristorcelli 2011 Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids. J. Turbul. 12 (49), 135.

T. Tanaka & J. Eaton 2007 A correction method for measuring turbulence kinetic energy dissipation rate by PIV. Exp. Fluids 42, 893902.

C. Tomkins , S. Kumar , G. Orlicz & K. Prestridge 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131150.

C. Tomkins , K. Prestridge , P. Rightley , M. Marr-Lyon , P. Vorobieff & R. Benjamin 2003 A quantitative study of the interaction of two Richtmyer–Meshkov-unstable gas cylinders. Phys. Fluids 15 (4), 9861004.

P. Vorobieff , N. G. Mohamed , C. Tomkins , C. Goodenough , M. Marr-Lyon & R. F. Benjamin 2003 Scaling evolution in shock-induced transition to turbulence. Phys. Rev. E 68 (6), 065301.

P. Vorobieff , P. M. Rightley & R. F. Benjamin 1998 Power-law spectra of incipient gas-curtain turbulence. Phys. Rev. Lett. 81 (11), 22402243.

P. Vorobieff , P. M. Rightley & R. F. Benjamin 1999 Shock-driven gas curtain: fractal dimension evolution in transition to turbulence. Physica D 133, 469476.

Z. Warhaft 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203240.

C. Weber , N. Haehn , J. Oakley , D. Rothamer & R. Bonazza 2012 Turbulent mixing measurements in the Richtmyer–Meshkov instability. Phys. Fluids 24, 074105.

F. Williams 1994 Combustion Theory. Perseus Books Publishing.

J. Yang , T. Kubota & E. E. Zukoski 1993 Applications of shock-induced mixing to supersonic combustion. AIAA J. 31 (5), 854862.

D. L. Youngs 1984 Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 3244.

N. J. Zabusky 1999 Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh–Taylor and Richtmyer–Meshkov environments. Annu. Rev. Fluid Mech. 31, 495536.

Y. Zhou , H. F. Robey & A. C. Buckingham 2003a Onset of turbulence in accelerated high-Reynolds-number flow. Phys. Rev. E 67, 056305.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: