Three-dimensional signatures of self-similarity in a high-energy-density plasma shear-driven mixing layer
Abstract
A hydrodynamic shear mixing layer experiment at the National Ignition Facility had previously demonstrated Eulerian scaling of integrated, late-time quantities, including turbulent kinetic energy. In this manuscript, the experiment is repeated with new materials. In this work, using the new dataset, we demonstrate that Euler-number scalings hold not just for late time, but dynamically throughout the experiment, for measurements in all three spatial dimensions. Incorporating the dynamic scaling leads to an enhanced calculation that the heavier of the two scaled experiments has approached three generations of mergers of its primary instability's structures and a consistent observation of such a merger in action in the lighter of the two scaled experiments. Furthermore, the improved scrutiny of the time evolution of instability structures leads to sharper estimates of turbulent kinetic energy, including a demonstration of different behaviors correlating with surface roughness (quantitatively consistent with transitions between laminar and turbulent initial states), as predicted by a Reynolds-averaged turbulent model, which evidently correctly handles the differing shock-roughness interactions to drive its internal state of the model into different regimes. Altogether, a picture arises of the analytical improvements in treating these variations (of times, densities, and roughnesses) as a unified whole and of multiple waysmore »
- Authors:
-
[1];
[1];
[1];
[1];
[2];
[1];
[1];
[2];
[1];
[1]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA). Office of Defense Programs (DP); USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
- OSTI Identifier:
- 1650620
- Alternate Identifier(s):
- OSTI ID: 1602337; OSTI ID: 1781371; OSTI ID: 1881605
- Report Number(s):
- LA-UR-19-26318; LA-UR-17-29376; LLNL-JRNL-838546
Journal ID: ISSN 1070-664X; TRN: US2202469
- Grant/Contract Number:
- 89233218CNA000001; AC52-07NA27344; AC52-06NA2539; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 27; Journal Issue: 3; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Viscosity; turbulence theory and modelling; turbulent flows; computational fluid dynamics; plasmas; fluid mixing; fluid flows; radiography
Citation Formats
Doss, F. W., Flippo, K. A., Merritt, E. C., DeVolder, B. G., Di Stefano, C. A., Huntington, C. M., Kline, J. L., Kot, L., Nagel, S. R., Rasmus, A. M., and Schmidt, D. W. Three-dimensional signatures of self-similarity in a high-energy-density plasma shear-driven mixing layer. United States: N. p., 2020.
Web. doi:10.1063/1.5122980.
Doss, F. W., Flippo, K. A., Merritt, E. C., DeVolder, B. G., Di Stefano, C. A., Huntington, C. M., Kline, J. L., Kot, L., Nagel, S. R., Rasmus, A. M., & Schmidt, D. W. Three-dimensional signatures of self-similarity in a high-energy-density plasma shear-driven mixing layer. United States. https://doi.org/10.1063/1.5122980
Doss, F. W., Flippo, K. A., Merritt, E. C., DeVolder, B. G., Di Stefano, C. A., Huntington, C. M., Kline, J. L., Kot, L., Nagel, S. R., Rasmus, A. M., and Schmidt, D. W. Mon .
"Three-dimensional signatures of self-similarity in a high-energy-density plasma shear-driven mixing layer". United States. https://doi.org/10.1063/1.5122980. https://www.osti.gov/servlets/purl/1650620.
@article{osti_1650620,
title = {Three-dimensional signatures of self-similarity in a high-energy-density plasma shear-driven mixing layer},
author = {Doss, F. W. and Flippo, K. A. and Merritt, E. C. and DeVolder, B. G. and Di Stefano, C. A. and Huntington, C. M. and Kline, J. L. and Kot, L. and Nagel, S. R. and Rasmus, A. M. and Schmidt, D. W.},
abstractNote = {A hydrodynamic shear mixing layer experiment at the National Ignition Facility had previously demonstrated Eulerian scaling of integrated, late-time quantities, including turbulent kinetic energy. In this manuscript, the experiment is repeated with new materials. In this work, using the new dataset, we demonstrate that Euler-number scalings hold not just for late time, but dynamically throughout the experiment, for measurements in all three spatial dimensions. Incorporating the dynamic scaling leads to an enhanced calculation that the heavier of the two scaled experiments has approached three generations of mergers of its primary instability's structures and a consistent observation of such a merger in action in the lighter of the two scaled experiments. Furthermore, the improved scrutiny of the time evolution of instability structures leads to sharper estimates of turbulent kinetic energy, including a demonstration of different behaviors correlating with surface roughness (quantitatively consistent with transitions between laminar and turbulent initial states), as predicted by a Reynolds-averaged turbulent model, which evidently correctly handles the differing shock-roughness interactions to drive its internal state of the model into different regimes. Altogether, a picture arises of the analytical improvements in treating these variations (of times, densities, and roughnesses) as a unified whole and of multiple ways by which deviations from the scaling could indicate an onset of non-hydrodynamic behavior. Such deviations were not expected for these experiments (which models correctly indicated would remain hydrodynamic) but could be introduced by, for example, imposing external fields or increasing drive energy to test conditions relevant to inertial confinement fusion or other high-energy-density experiments.},
doi = {10.1063/1.5122980},
journal = {Physics of Plasmas},
number = 3,
volume = 27,
place = {United States},
year = {Mon Mar 02 00:00:00 EST 2020},
month = {Mon Mar 02 00:00:00 EST 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 3 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Observation of a Kelvin-Helmholtz Instability in a High-Energy-Density Plasma on the Omega Laser
journal, July 2009
- Harding, E. C.; Hansen, J. F.; Hurricane, O. A.
- Physical Review Letters, Vol. 103, Issue 4
Spanwise scale selection in plane mixing layers
journal, February 1993
- Rogers, Michael M.; Moser, Robert D.
- Journal of Fluid Mechanics, Vol. 247
The mixing transition in turbulent flows
journal, April 2000
- Dimotakis, Paul E.
- Journal of Fluid Mechanics, Vol. 409
Development of a two-stream mixing layer from tripped and untripped boundary layers
journal, December 1990
- Bell, James H.; Mehta, Rabindra D.
- AIAA Journal, Vol. 28, Issue 12
On the origin and evolution of streamwise vortical structures in a plane, free shear layer
journal, November 1986
- Lasheras, J. C.; Cho, J. S.; Maxworthy, T.
- Journal of Fluid Mechanics, Vol. 172, Issue -1
X-ray Doppler Velocimetry: An imaging diagnostic of 3D fluid flow in turbulent plasma
journal, June 2017
- Koch, J. A.; Field, J. E.; Kilkenny, J. D.
- High Energy Density Physics, Vol. 23
The National Ignition Facility: Status and Plans for Laser Fusion and High-Energy-Density Experimental Studies
journal, May 2003
- Moses, Edward I.; Wuest, Craig R.
- Fusion Science and Technology, Vol. 43, Issue 3
Development and validation of a turbulent-mix model for variable-density and compressible flows
journal, October 2010
- Banerjee, Arindam; Gore, Robert A.; Andrews, Malcolm J.
- Physical Review E, Vol. 82, Issue 4
Growth of the two-dimensional mixing layer from a turbulent and nonturbulent boundary layer
journal, January 1979
- Browand, F. K.; Latigo, B. O.
- Physics of Fluids, Vol. 22, Issue 6
Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow
journal, April 2011
- Hahn, M.; Drikakis, D.; Youngs, D. L.
- Physics of Fluids, Vol. 23, Issue 4
The effect of a short-wavelength mode on the evolution of a long-wavelength perturbation driven by a strong blast wave
journal, December 2004
- Miles, A. R.; Edwards, M. J.; Blue, B.
- Physics of Plasmas, Vol. 11, Issue 12
Small-scale transition in a plane mixing layer
journal, January 1990
- Huang, Lein-Saing; Ho, Chih-Ming
- Journal of Fluid Mechanics, Vol. 210
Secondary instability of a temporally growing mixing layer
journal, November 1987
- Metcalfe, Ralph W.; Orszag, Steven A.; Brachet, Marc E.
- Journal of Fluid Mechanics, Vol. 184
The Crystal Backlighter Imager: A spherically bent crystal imager for radiography on the National Ignition Facility
journal, January 2019
- Hall, G. N.; Krauland, C. M.; Schollmeier, M. S.
- Review of Scientific Instruments, Vol. 90, Issue 1
Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids
journal, January 2011
- Schwarzkopf, John D.; Livescu, Daniel; Gore, Robert A.
- Journal of Turbulence, Vol. 12
Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations
journal, August 2007
- Zhou, Ye
- Physics of Plasmas, Vol. 14, Issue 8
Reynolds averaged Navier-Stokes simulations of compressible mixing layers of similar and dissimilar gases: Performance of k– ɛ turbulence model
journal, November 2014
- Javed, Afroz; Rajan, Nks; Chakraborty, Debasis
- Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 229, Issue 9
Increasing shot and data collection rates of the Shock/Shear experiment at the National Ignition Facility
journal, May 2016
- Doss, F. W.; Flippo, K. A.; Capelli, D.
- Journal of Physics: Conference Series, Vol. 717
Calibrating mix models for NIF tuning
journal, August 2010
- Hoffman, Nelson M.; Hammel, Bruce A.; Schilling, Oleg
- Journal of Physics: Conference Series, Vol. 244, Issue 2
The density of organized vortices in a turbulent mixing layer
journal, June 1975
- Moore, D. W.; Saffman, P. G.
- Journal of Fluid Mechanics, Vol. 69, Issue 3
On the turbulence structure in inert and reacting compressible mixing layers
journal, November 2007
- Mahle, Inga; Foysi, Holger; Sarkar, Sutanu
- Journal of Fluid Mechanics, Vol. 593
Metrics for long wavelength asymmetries in inertial confinement fusion implosions on the National Ignition Facility
journal, April 2014
- Kritcher, A. L.; Town, R.; Bradley, D.
- Physics of Plasmas, Vol. 21, Issue 4
The effect of turbulent kinetic energy on inferred ion temperature from neutron spectra
journal, July 2014
- Murphy, T. J.
- Physics of Plasmas, Vol. 21, Issue 7
Particle dynamics and mixing in a viscously decaying shear layer
journal, June 1991
- Meiburg, E.; Newton, P. K.
- Journal of Fluid Mechanics, Vol. 227
Instability, mixing, and transition to turbulence in a laser-driven counterflowing shear experiment
journal, January 2013
- Doss, F. W.; Loomis, E. N.; Welser-Sherrill, L.
- Physics of Plasmas, Vol. 20, Issue 1
Modifying mixing and instability growth through the adjustment of initial conditions in a high-energy-density counter-propagating shear experiment on OMEGA
journal, June 2015
- Merritt, E. C.; Doss, F. W.; Loomis, E. N.
- Physics of Plasmas, Vol. 22, Issue 6
Development of the CD Symcap platform to study gas-shell mix in implosions at the National Ignition Facility
journal, September 2014
- Casey, D. T.; Smalyuk, V. A.; Tipton, R. E.
- Physics of Plasmas, Vol. 21, Issue 9
The Laser-Driven X-ray Big Area Backlighter (BABL): Design, Optimization, and Evolution
journal, May 2016
- Flippo, Kirk; DeVolder, Barbara; Doss, Forrest
- Journal of Physics: Conference Series, Vol. 717
Structure in turbulent mixing layers and wakes using a chemical reaction
journal, August 1981
- Breidenthal, R.
- Journal of Fluid Mechanics, Vol. 109
Evolution of surface structure in laser-preheated perturbed materials
journal, February 2017
- Di Stefano, C. A.; Merritt, E. C.; Doss, F. W.
- Physical Review E, Vol. 95, Issue 2
The compressible turbulent shear layer: an experimental study
journal, December 1988
- Papamoschou, Dimitri; Roshko, Anatol
- Journal of Fluid Mechanics, Vol. 197
Observation and analysis of emergent coherent structures in a high-energy-density shock-driven planar mixing layer experiment
journal, August 2016
- Doss, F. W.; Flippo, K. A.; Merritt, E. C.
- Physical Review E, Vol. 94, Issue 2
Observation of dual-mode, Kelvin-Helmholtz instability vortex merger in a compressible flow
journal, May 2017
- Wan, W. C.; Malamud, G.; Shimony, A.
- Physics of Plasmas, Vol. 24, Issue 5
Three- and two-dimensional simulations of counter-propagating shear experiments at high energy densities at the National Ignition Facility
journal, November 2015
- Wang, Ping; Zhou, Ye; MacLaren, Stephan A.
- Physics of Plasmas, Vol. 22, Issue 11
The Shock/Shear platform for planar radiation-hydrodynamics experiments on the National Ignition Facilitya)
journal, May 2015
- Doss, F. W.; Kline, J. L.; Flippo, K. A.
- Physics of Plasmas, Vol. 22, Issue 5
Two classes of Richtmyer-Meshkov instabilities: A detailed statistical look
journal, April 2013
- Ristorcelli, J. R.; Gowardhan, A. A.; Grinstein, F. F.
- Physics of Fluids, Vol. 25, Issue 4
Three-dimensional hydrodynamics of the deceleration stage in inertial confinement fusion
journal, March 2015
- Weber, C. R.; Clark, D. S.; Cook, A. W.
- Physics of Plasmas, Vol. 22, Issue 3
Observation of mix in a compressible plasma in a convergent cylindrical geometry
journal, November 2002
- Barnes, Cris W.; Batha, S. H.; Dunne, A. M.
- Physics of Plasmas, Vol. 9, Issue 11
Three-dimensional instability of Burgers and Lamb–Oseen vortices in a strain field
journal, January 1999
- Eloy, Christophe; Le DizÈS, StÉPhane
- Journal of Fluid Mechanics, Vol. 378
Effect of free-stream turbulence on large structure in turbulent mixing layers
journal, April 1978
- Chandrsuda, C.; Mehta, R. D.; Weir, A. D.
- Journal of Fluid Mechanics, Vol. 85, Issue 4
K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities
journal, August 2006
- Dimonte, Guy; Tipton, Robert
- Physics of Fluids, Vol. 18, Issue 8
Two-dimensional shear-layer entrainment
journal, November 1986
- Dimotakis, Paul E.
- AIAA Journal, Vol. 24, Issue 11
The RAGE radiation-hydrodynamic code
journal, October 2008
- Gittings, Michael; Weaver, Robert; Clover, Michael
- Computational Science & Discovery, Vol. 1, Issue 1
Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities
journal, April 2015
- Morgan, Brandon E.; Wickett, Michael E.
- Physical Review E, Vol. 91, Issue 4
Turbulent shear-layer 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
Three-dimensional instability during vortex merging
journal, October 2001
- Meunier, Patrice; Leweke, Thomas
- Physics of Fluids, Vol. 13, Issue 10
The numerical computation of turbulent flows
journal, March 1974
- Launder, B. E.; Spalding, D. B.
- Computer Methods in Applied Mechanics and Engineering, Vol. 3, Issue 2
Streamwise vortex structure in plane mixing layers
journal, September 1986
- Bernal, L. P.; Roshko, A.
- Journal of Fluid Mechanics, Vol. 170
Plasma transport in an Eulerian AMR code
journal, April 2017
- Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.
- Physics of Plasmas, Vol. 24, Issue 4
Effects of residual kinetic energy on yield degradation and ion temperature asymmetries in inertial confinement fusion implosions
journal, May 2018
- Woo, K. M.; Betti, R.; Shvarts, D.
- Physics of Plasmas, Vol. 25, Issue 5
Sudden Viscous Dissipation of Compressing Turbulence
journal, March 2016
- Davidovits, Seth; Fisch, Nathaniel J.
- Physical Review Letters, Vol. 116, Issue 10
Exponential yield sensitivity to long-wavelength asymmetries in three-dimensional simulations of inertial confinement fusion capsule implosions
journal, August 2015
- Haines, Brian M.
- Physics of Plasmas, Vol. 22, Issue 8
Bemerkungen über die Entstehung der Turbulenz
journal, January 1921
- Prandtl, L.
- ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 1, Issue 6
Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation
journal, May 2014
- Weber, C. R.; Clark, D. S.; Cook, A. W.
- Physical Review E, Vol. 89, Issue 5
Layer Some Measurements on the Effect of Tripping the Two-Dimensional Shear
journal, February 1975
- Batt, Richard G.
- AIAA Journal, Vol. 13, Issue 2
Ablative stabilization of Rayleigh-Taylor instabilities resulting from a laser-driven radiative shock
journal, May 2018
- Huntington, C. M.; Shimony, A.; Trantham, M.
- Physics of Plasmas, Vol. 25, Issue 5
Plasma kinetic effects on interfacial mix
journal, November 2016
- Yin, L.; Albright, B. J.; Taitano, W.
- Physics of Plasmas, Vol. 23, Issue 11
Three-dimensional simulation of a Richtmyer–Meshkov instability with a two-scale initial perturbation
journal, October 2002
- Cohen, Ronald H.; Dannevik, William P.; Dimits, Andris M.
- Physics of Fluids, Vol. 14, Issue 10
Three-dimensional simulation strategy to determine the effects of turbulent mixing on inertial-confinement-fusion capsule performance
journal, May 2014
- Haines, Brian M.; Grinstein, Fernando F.; Fincke, James R.
- Physical Review E, Vol. 89, Issue 5
A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability
journal, September 1990
- Gauthier, Serge; Bonnet, Michel
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 9
The effect of mix on capsule yields as a function of shell thickness and gas fill
journal, June 2014
- Bradley, P. A.
- Physics of Plasmas, Vol. 21, Issue 6
A spanwise structure in the plane shear layer
journal, July 1983
- Jimenez, Javier
- Journal of Fluid Mechanics, Vol. 132
Drive Asymmetry and the Origin of Turbulence in an ICF Implosion
journal, August 2012
- Thomas, V. A.; Kares, R. J.
- Physical Review Letters, Vol. 109, Issue 7
Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number
journal, April 1974
- Winant, C. D.; Browand, F. K.
- Journal of Fluid Mechanics, Vol. 63, Issue 02
Late-time mixing and turbulent behavior in high-energy-density shear experiments at high Atwood numbers
journal, May 2018
- Flippo, K. A.; Doss, F. W.; Merritt, E. C.
- Physics of Plasmas, Vol. 25, Issue 5
The mixing layer at high Reynolds number: large-structure dynamics and entrainment
journal, December 1976
- Dimotakis, Paul E.; Brown, Garry L.
- Journal of Fluid Mechanics, Vol. 78, Issue 3
The National Ignition Facility modular Kirkpatrick-Baez microscope
journal, August 2016
- Pickworth, L. A.; Ayers, J.; Bell, P.
- Review of Scientific Instruments, Vol. 87, Issue 11
Two laser-driven mix experiments to study reshock and shear
journal, September 2013
- Welser-Sherrill, L.; Fincke, J.; Doss, F.
- High Energy Density Physics, Vol. 9, Issue 3
The physics of long- and intermediate-wavelength asymmetries of the hot spot: Compression hydrodynamics and energetics
journal, October 2017
- Bose, A.; Betti, R.; Shvarts, D.
- Physics of Plasmas, Vol. 24, Issue 10
The three-dimensional instability of strained vortices in a viscous fluid
journal, January 1987
- Landman, M. J.; Saffman, P. G.
- Physics of Fluids, Vol. 30, Issue 8
About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity
journal, September 2007
- Schmitt, François G.
- Comptes Rendus Mécanique, Vol. 335, Issue 9-10
The two- and three-dimensional instabilities of a spatially periodic shear layer
journal, January 1982
- Pierrehumbert, R. T.; Widnall, S. E.
- Journal of Fluid Mechanics, Vol. 114, Issue -1
Modeling of Rayleigh-Taylor mixing using single-fluid models
journal, January 2019
- Kokkinakis, Ioannis W.; Drikakis, Dimitris; Youngs, David L.
- Physical Review E, Vol. 99, Issue 1
Measurements of the streamwise vortical structures in a plane mixing layer
journal, June 1992
- Bell, James H.; Mehta, Rabindra D.
- Journal of Fluid Mechanics, Vol. 239, Issue -1
On the Stability, or Instability, of certain Fluid Motions
journal, November 1879
- Rayleigh, Lord
- Proceedings of the London Mathematical Society, Vol. s1-11, Issue 1
Development of a Big Area BackLighter for high energy density experiments
journal, September 2014
- Flippo, K. A.; Kline, J. L.; Doss, F. W.
- Review of Scientific Instruments, Vol. 85, Issue 9
Large‐ and small‐scale stirring of vorticity and a passive scalar in a 3‐D temporal mixing layer
journal, December 1992
- Comte, Pierre; Lesieur, Marcel; Lamballais, Eric
- Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 12
Late-Time Mixing Sensitivity to Initial Broadband Surface Roughness in High-Energy-Density Shear Layers
journal, November 2016
- Flippo, K. A.; Doss, F. W.; Kline, J. L.
- Physical Review Letters, Vol. 117, Issue 22
Three-Dimensional Instability of Elliptical Flow
journal, October 1986
- Bayly, B. J.
- Physical Review Letters, Vol. 57, Issue 17
On a Disturbing Infinity in Lord Rayleigh's Solution for Waves in a Plane Vortex Stratum1
journal, November 1880
- ,
- Nature, Vol. 23, Issue 576, p. 45-46
Onset of nonlinear saturation for Rayleigh-Taylor growth in the presence of a full spectrum of modes
journal, June 1989
- Haan, Steven W.
- Physical Review A, Vol. 39, Issue 11
The Los Alamos suite of relativistic atomic physics codes
journal, May 2015
- Fontes, C. J.; Zhang, H. L.; Jr, J. Abdallah
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 48, Issue 14
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
journal, September 2015
- Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.
- Flow, Turbulence and Combustion, Vol. 96, Issue 1
Compressibility Effects in Turbulent Shear Layers
journal, June 1983
- Bogdanoff, D. W.
- AIAA Journal, Vol. 21, Issue 6
The influence of asymmetry on mix in direct-drive inertial confinement fusion experiments
journal, May 2004
- Christensen, C. R.; Wilson, D. C.; Barnes, Cris W.
- Physics of Plasmas, Vol. 11, Issue 5
Validation of a Turbulent Kelvin-Helmholtz Shear Layer Model Using a High-Energy-Density OMEGA Laser Experiment
journal, October 2012
- Hurricane, O. A.; Smalyuk, V. A.; Raman, K.
- Physical Review Letters, Vol. 109, Issue 15
The time scale for the transition to turbulence in a high Reynolds number, accelerated flow
journal, March 2003
- Robey, H. F.; Zhou, Ye; Buckingham, A. C.
- Physics of Plasmas, Vol. 10, Issue 3
XLIII. On discontinuous movements of fluids
journal, November 1868
- Helmholtz,
- The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 36, Issue 244
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