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Flux correlations in supersonic isothermal turbulence

  • R. Wagner (a1), G. Falkovich (a2), A. G. Kritsuk (a3) and M. L. Norman (a1) (a3)

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.

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AluieH. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106 (17), 174502.
AluieH., LiS. & LiH. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29.
BahraminasabA., NiryM. D., DavoudiJ., Reza Rahimi TabarM., MasoudiA. A. & SreenivasanK. R. 2008 Taylor’s frozen-flow hypothesis in Burgers turbulence. Phys. Rev. E 77, 065302.
BenziR., BiferaleL., FisherR. T., KadanoffL. P., LambD. Q. & ToschiF. 2008 Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev. Lett. 100 (23), 234503.
BrandenburgA. & NordlundÅ 2011 Astrophysical turbulence modelling. Rep. Prog. Phys. 74 (4), 046901.
ColellaP. & WoodwardP. R. 1984 The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54, 174201.
ElmegreenB. G. & ScaloJ. 2004 Interstellar turbulence I: observations and processes. Annu. Rev. Astron. Astrophys. 42, 211273.
FalkovichG., FouxonI. & OzY. 2010 New relations for correlation functions in Navier–Stokes turbulence. J. Fluid Mech. 644, 465472.
GaltierS. & BanerjeeS. 2011 Exact relation for correlation functions in compressible isothermal turbulence. Phys. Rev. Lett. 107 (13), 134501.
HeyerM. H. & BruntC. M. 2004 The universality of turbulence in galactic molecular clouds. Astrophys. J. Lett. 615, L45L48.
KitsionasS., FederrathC., KlessenR. S., SchmidtW., PriceD. J., DursiL. J., GritschnederM., WalchS., PiontekR., KimJ., JappsenA.-K., CiecielagP. & Mac LowM.-M. 2009 Algorithmic comparisons of decaying, isothermal, supersonic turbulence. Astron. Astrophys. 508, 541560.
KolmogorovA. N. 1941 Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 19.
KritsukA. G., NordlundÅ, CollinsD., PadoanP., NormanM. L., AbelT., BanerjeeR., FederrathC., FlockM., LeeD., LiP. S., MüllerW.-C., TeyssierR., UstyugovS. D., VogelC. & XuH. 2011 Comparing numerical methods for isothermal magnetized supersonic turbulence. Astrophys. J. 737, 13.
KritsukA. G., NormanM. L., PadoanP. & WagnerR. 2007a The statistics of supersonic isothermal turbulence. Astrophys. J. 665, 416431.
KritsukA. G., PadoanP., WagnerR. & NormanM. 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. 393399.
McKeeC. F. & OstrikerE. C. 2007 Theory of star formation. Annu. Rev. Astron. Astrophys. 45, 565687.
MitraD., BecJ., PanditR. & FrischU. 2005 Is multiscaling an artifact in the stochastically forced Burgers equation? Phys. Rev. Lett. 94 (19), 194501.
NormanM. L., BryanG. L., HarknessR., BordnerJ., ReynoldsD., O’SheaB. & WagnerR. 2007 Simulating cosmological evolution with Enzo. In Petascale Computing: Algorithms and Applications (ed. Bader David A.). pp. 83102, CRC.
PanL., PadoanP. & KritsukA. G. 2009 Dissipative structures in supersonic turbulence. Phys. Rev. Lett. 102 (3), 034501.
PorterD., PouquetA. & WoodwardP. 2002 Measures of intermittency in driven supersonic flows. Phys. Rev. E 66 (2), 026301.
SchmidtW., FederrathC. & KlessenR. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101 (19), 194505.
SytineI. V., PorterD. H., WoodwardP. R., HodsonS. W. & WinklerK.-H. 2000 Convergence tests for the piecewise parabolic method and Navier–Stokes solutions for homogeneous compressible turbulence. J. Comput. Phys. 158, 225238.
WangJ., WangL.-P., XiaoZ., ShiY. & ChenS. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229, 52575279.
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