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Astrophysics > Astrophysics of Galaxies

arXiv:1306.5768 (astro-ph)
[Submitted on 24 Jun 2013 (v1), last revised 11 Jul 2013 (this version, v2)]

Title:Energy cascade and scaling in supersonic isothermal turbulence

Authors:Alexei G. Kritsuk, Rick Wagner, Michael L. Norman
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Abstract:Supersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier-Stokes equations (Galtier and Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-fifths law exist describing fifth- and fourth-order correlations, but only the fourth-order relation remains `universal' in a wide range of Mach numbers from incompressible to highly compressible regimes. A new approximate relation valid in the strongly supersonic regime is derived and verified. We also briefly discuss the origin of bottleneck bumps in simulations of compressible turbulence.
Comments: Accepted to JFM Rapids, 11 pages, 6 figures
Subjects: Astrophysics of Galaxies (astro-ph.GA); Fluid Dynamics (physics.flu-dyn)
Cite as: arXiv:1306.5768 [astro-ph.GA]
  (or arXiv:1306.5768v2 [astro-ph.GA] for this version)
  https://doi.org/10.48550/arXiv.1306.5768
Journal reference: J. Fluid Mech., 729 (2013), R1
Related DOI: https://doi.org/10.1017/jfm.2013.342

Submission history

From: Alexei Kritsuk [view email]
[v1] Mon, 24 Jun 2013 20:13:00 UTC (53 KB)
[v2] Thu, 11 Jul 2013 19:52:33 UTC (37 KB)
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