Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-19T12:00:13.171Z Has data issue: false hasContentIssue false
  • English
  • Français

Flux correlations in supersonic isothermal turbulence

Published online by Cambridge University Press:  17 October 2012

R. Wagner ,
G. Falkovich ,
A. G. Kritsuk  and
M. L. Norman
R. Wagner*
Affiliation:
San Diego Supercomputer Center, University of California, San Diego, MC 0505, 10100 Hopkins Drive, La Jolla, CA 92093-0505, USA
G. Falkovich
Affiliation:
Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
A. G. Kritsuk
Affiliation:
Department of Physics and Center for Astrophysics and Space Sciences, University of California, San Diego, MC 0424, 9500 Gilman Drive, La Jolla, CA 92093-0424, USA
M. L. Norman
Affiliation:
San Diego Supercomputer Center, University of California, San Diego, MC 0505, 10100 Hopkins Drive, La Jolla, CA 92093-0505, USA Department of Physics and Center for Astrophysics and Space Sciences, University of California, San Diego, MC 0424, 9500 Gilman Drive, La Jolla, CA 92093-0424, USA
*
†Email address for correspondence: rpwagner@sdsc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier–Stokes equation by Falkovich, Fouxon & Oz (J. Fluid Mech., vol. 644, 2010, p. 465). That relation, for compressible barotropic fluids, was derived assuming turbulence generated by a large-scale force. However, compressible turbulence in simulations is usually initialized and maintained by a large-scale acceleration, as in gravity-driven astrophysical flows. We present a new approximate flux relation for isothermal turbulence driven by a large-scale acceleration, and find it in reasonable agreement with the simulation results.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 482 - 490
Copyright
©2012 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 (17), 174502.Google Scholar
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29.Google Scholar
Bahraminasab, A., Niry, M. D., Davoudi, J., Reza Rahimi Tabar, M., Masoudi, A. A. & Sreenivasan, K. R. 2008 Taylor’s frozen-flow hypothesis in Burgers turbulence. Phys. Rev. E 77, 065302.Google 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 (23), 234503.Google Scholar
Brandenburg, A. & Nordlund, Å 2011 Astrophysical turbulence modelling. Rep. Prog. Phys. 74 (4), 046901.Google Scholar
Colella, P. & Woodward, P. R. 1984 The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54, 174–201.Google Scholar
Elmegreen, B. G. & Scalo, J. 2004 Interstellar turbulence I: observations and processes. Annu. Rev. Astron. Astrophys. 42, 211–273.Google Scholar
Falkovich, G., Fouxon, I. & Oz, Y. 2010 New relations for correlation functions in Navier–Stokes turbulence. J. Fluid Mech. 644, 465–472.CrossRefGoogle Scholar
Galtier, S. & Banerjee, S. 2011 Exact relation for correlation functions in compressible isothermal turbulence. Phys. Rev. Lett. 107 (13), 134501.Google Scholar
Heyer, M. H. & Brunt, C. M. 2004 The universality of turbulence in galactic molecular clouds. Astrophys. J. Lett. 615, L45–L48.Google Scholar
Kitsionas, S., Federrath, C., Klessen, R. S., Schmidt, W., Price, D. J., Dursi, L. J., Gritschneder, M., Walch, S., Piontek, R., Kim, J., Jappsen, A.-K., Ciecielag, P. & Mac Low, M.-M. 2009 Algorithmic comparisons of decaying, isothermal, supersonic turbulence. Astron. Astrophys. 508, 541–560.Google Scholar
Kolmogorov, A. N. 1941 Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 19.Google Scholar
Kritsuk, A. G., Nordlund, Å, Collins, D., Padoan, P., Norman, M. L., Abel, T., Banerjee, R., Federrath, C., Flock, M., Lee, D., Li, P. S., Müller, W.-C., Teyssier, R., Ustyugov, S. D., Vogel, C. & Xu, H. 2011 Comparing numerical methods for isothermal magnetized supersonic turbulence. Astrophys. J. 737, 13.Google Scholar
Kritsuk, A. G., Norman, M. L., Padoan, P. & Wagner, R. 2007a The statistics of supersonic isothermal turbulence. Astrophys. J. 665, 416–431.Google Scholar
Kritsuk, A. G., Padoan, P., Wagner, R. & Norman, M. L. 2007b Scaling laws and intermittency in highly compressible turbulence. In Turbulence and Nonlinear Processes in Astrophysical Plasmas (ed. Shaikh, D. & Zank, G. P.). American Institute of Physics Conference Series , vol. 932,. pp. 393–399.Google Scholar
McKee, C. F. & Ostriker, E. C. 2007 Theory of star formation. Annu. Rev. Astron. Astrophys. 45, 565–687.Google Scholar
Mitra, D., Bec, J., Pandit, R. & Frisch, U. 2005 Is multiscaling an artifact in the stochastically forced Burgers equation? Phys. Rev. Lett. 94 (19), 194501.CrossRefGoogle ScholarPubMed
Norman, M. L., Bryan, G. L., Harkness, R., Bordner, J., Reynolds, D., O’Shea, B. & Wagner, R. 2007 Simulating cosmological evolution with Enzo. In Petascale Computing: Algorithms and Applications (ed. Bader, David A.). pp. 83–102, CRC.Google Scholar
Pan, L., Padoan, P. & Kritsuk, A. G. 2009 Dissipative structures in supersonic turbulence. Phys. Rev. Lett. 102 (3), 034501.Google Scholar
Porter, D., Pouquet, A. & Woodward, P. 2002 Measures of intermittency in driven supersonic flows. Phys. Rev. E 66 (2), 026301.Google Scholar
Schmidt, W., Federrath, C. & Klessen, R. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101 (19), 194505.Google Scholar
Sytine, I. V., Porter, D. H., Woodward, P. R., Hodson, S. W. & Winkler, K.-H. 2000 Convergence tests for the piecewise parabolic method and Navier–Stokes solutions for homogeneous compressible turbulence. J. Comput. Phys. 158, 225–238.Google Scholar
Wang, J., Wang, L.-P., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229, 5257–5279.Google Scholar