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Energy cascade and scaling in supersonic isothermal turbulence

Published online by Cambridge University Press:  22 July 2013

Alexei G. Kritsuk ,
Rick Wagner  and
Michael L. Norman
Alexei 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
Rick Wagner
Affiliation:
San Diego Supercomputer Center, University of California, San Diego, MC 0505, 10100 Hopkins Drive, La Jolla, CA 92093-0505, USA
Michael L. Norman
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 San Diego Supercomputer Center, University of California, San Diego, MC 0505, 10100 Hopkins Drive, La Jolla, CA 92093-0505, USA
*
†Email address for correspondence: [email protected]
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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 & 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.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , R1
Copyright
©2013 Cambridge University Press 

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