Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-20T00:43:18.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Intermittency caused by compressibility: a Lagrangian study

Published online by Cambridge University Press:  07 December 2015

Yantao Yang ,
Jianchun Wang ,
Yipeng Shi ,
Zuoli Xiao ,
X. T. He  and
Shiyi Chen
Yantao Yang
Affiliation:
State Key Laboratory for Turbulence and Complex System, HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Jianchun Wang
Affiliation:
State Key Laboratory for Turbulence and Complex System, HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China
Yipeng Shi*
Affiliation:
State Key Laboratory for Turbulence and Complex System, HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China
Zuoli Xiao
Affiliation:
State Key Laboratory for Turbulence and Complex System, HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China
X. T. He
Affiliation:
State Key Laboratory for Turbulence and Complex System, HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex System, HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China South University of Science and Technology of China, Shenzhen 518055, PR China Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100191, PR China
*
†Email address for correspondence: ypshi@coe.pku.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate how compressibility affects the turbulent statistics from a Lagrangian point of view, particularly in the parameter range where the flow transits from the incompressible type to a state dominated by shocklets. A series of three-dimensional simulations were conducted for different types of driving and several Mach numbers. For purely solenoidal driving, as the Mach number increases a new self-similar region first emerges in the Lagrangian structure functions at sub-Kolmogorov time scale and gradually extends to larger time scale. In this region the relative scaling exponent saturates and the saturated value decreases as the compressibility becomes stronger, which can be attributed to the shocklets. The scaling exponent for the inertial range is still very close to that of incompressible turbulence for small Mach number, and discrepancy becomes visible when the Mach number is high enough. When the driving force is dominated by the compressive component the shocklet-induced self-similar region occupies a much wider range of time scales than that in the purely solenoidal driving case. Regardless of the type of driving force, the probability density functions of the velocity increment collapse onto one another for the time scales in the new self-similar region after proper normalization.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Homogeneous turbulence Turbulent Flows: Intermittency
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , R6
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.CrossRefGoogle ScholarPubMed
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751 (2), L29.Google Scholar
Arnèodo, A., Benzi, R., Berg, J., Biferale, L., Bodenschatz, E., Busse, A., Calzavarini, E., Castaing, B., Cencini, M., Chevillard, L., Fisher, R. T., Grauer, R., Homann, H., Lamb, D., Lanotte, A. S., Lévèque, E., Lüthi, B., Mann, J., Mordant, N., Müller, W.-C., Ott, S., Ouellette, N. T., Pinton, J.-F., Pope, S. B., Roux, S. G., Toschi, F., Xu, H. & Yeung, P. K. 2008 Universal intermittent properties of particle trajectories in highly turbulent flows. Phys. Rev. Lett. 100, 254504.Google Scholar
Banerjee, S. & Galtier, S. 2013 Exact relation with two-point correlation functions and phenomenological approach for compressible magnetohydrodynamic turbulence. Phys. Rev. E 87, 013019.Google Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S. & Toschi, F. 2006 Effects of vortex filaments on the velocity of tracers and heavy particles in turbulence. Phys. Fluids 18 (8), 081702.Google Scholar
Benzi, R., Biferale, L., Fisher, R., Lamb, D. Q. & Toschi, F. 2010 Inertial range Eulerian and Lagrangian statistics from numerical simulations of isotropic turbulence. J. Fluid Mech. 653, 221–244.CrossRefGoogle Scholar
Benzi, R., Biferale, L., Fisher, R. T., Kadanoff, L. P., Lamb, D. Q. & Toschi, F. 2008 Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev. Lett. 100, 234503.CrossRefGoogle ScholarPubMed
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48, R29–R32.Google Scholar
Biferale, L., Bodenschatz, E., Cencini, M., Lanotte, A. S., Ouellette, N. T., Toschi, F. & Xu, H. 2008 Lagrangian structure functions in turbulence: a quantitative comparison between experiment and direct numerical simulation. Phys. Fluids 20 (6), 065103.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Lanotte, A. & Toschi, F. 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17 (2), 021701.Google Scholar
Falkovich, G., Xu, H., Pumir, A., Bodenschatz, E., Biferale, L., Boffetta, G., Lanotte, A. S. & Toschi, F. 2012 On Lagrangian single-particle statistics. Phys. Fluids 24 (5), 055102.Google Scholar
Federrath, C. 2013 On the universality of supersonic turbulence. Mon. Not. R. Astron. Soc. 436 (2), 1245–1257.Google Scholar
Federrath, C., Roman-Duval, J., Klessen, R. S., Schmidt, W. & Mac Low, M. M. 2010 Comparing the statistics of interstellar turbulence in simulations and observations. Astron. Astrophys. 512, A81.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Galtier, S. & Banerjee, S. 2011 Exact relation for correlation functions in compressible isothermal turbulence. Phys. Rev. Lett. 107, 134501.Google Scholar
Hennebelle, P. & Falgarone, E. 2012 Turbulent molecular clouds. Astron. Astrophys. Rev. 20 (1), 55.Google Scholar
Huang, Y., Biferale, L., Calzavarini, E., Sun, C. & Toschi, F. 2013 Lagrangian single-particle turbulent statistics through the Hilbert–Huang transform. Phys. Rev. E 87, 041003.Google Scholar
Konstandin, L., Federrath, C., Klessen, R. S. & Schmidt, W. 2012 Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks. J. Fluid Mech. 692, 183–206.Google Scholar
Kritsuk, A. G., Norman, M. L., Padoan, P. & Wagner, R. 2007 The statistics of supersonic isothermal turbulence. Astrophys. J. 665 (1), 416–431.Google Scholar
Kritsuk, A. G., Wagner, R. & Norman, M. L. 2013 Energy cascade and scaling in supersonic isothermal turbulence. J. Fluid Mech. 729, R1.Google Scholar
Lanotte, A. S., Biferale, L., Boffetta, G. & Toschi, F. 2013 A new assessment of the second-order moment of Lagrangian velocity increments in turbulence. J. Turbul. 14 (7), 34–48.Google Scholar
Lévêque, E. & Naso, A. 2014 Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence. Europhys. Lett. 108 (5), 54004.Google Scholar
McKee, C. F. & Ostriker, E. C. 2007 Theory of star formation. Annu. Rev. Astron. Astrophys. 45 (1), 565–687.Google Scholar
Padoan, P. & Nordlund, Å. 2002 The stellar initial mass function from turbulent fragmentation. Astrophys. J. 576 (2), 870.Google Scholar
Pan, L., Padoan, P. & Kritsuk, A. G. 2009 Dissipative structures in supersonic turbulence. Phys. Rev. Lett. 102, 034501.Google Scholar
Samtaney, R., Pullin, D. I. & Kosović, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13 (5), 1415–1430.CrossRefGoogle Scholar
Scalo, J. & Elmegreen, B. G. 2004 Interstellar turbulence. Part II: implications and effects. Annu. Rev. Astron. Astrophys. 42, 275–316.Google Scholar
Schmidt, W., Federrath, C. & Klessen, R. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101, 194505.Google Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41 (1), 375–404.Google Scholar
Wagner, R., Falkovich, G., Kritsuk, A. G. & Norman, M. L. 2012 Flux correlations in supersonic isothermal turbulence. J. Fluid Mech. 713, 482–490.Google Scholar
Wang, J., Shi, Y., Wang, L., Xiao, Z., He, X. T. & Chen, S. 2011 Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence. Phys. Fluids 23 (12), 125103.Google Scholar
Wang, J., Shi, Y., Wang, L., Xiao, Z., He, X. T. & Chen, S. 2012 Scaling and statistics in three-dimensional compressible turbulence. Phys. Rev. Lett. 108, 214505.Google Scholar
Wang, J., Wang, L., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229, 5257–5279.Google Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2013a Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505.Google Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2013b Statistics and structures of pressure and density in compressible isotropic turbulence. J. Turbul. 14 (6), 21–37.CrossRefGoogle Scholar
Yang, Y., Wang, J., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2013 Acceleration of passive tracers in compressible turbulent flow. Phys. Rev. Lett. 110, 064503.CrossRefGoogle ScholarPubMed