Energy cascade and scaling in supersonic isothermal turbulence
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.
Keywords
Cite
@article{arxiv.1306.5768,
title = {Energy cascade and scaling in supersonic isothermal turbulence},
author = {Alexei G. Kritsuk and Rick Wagner and Michael L. Norman},
journal= {arXiv preprint arXiv:1306.5768},
year = {2013}
}
Comments
Accepted to JFM Rapids, 11 pages, 6 figures