Energy cascade and scaling in supersonic isothermal turbulence
arXiv:1306.5768 · doi:10.1017/jfm.2013.342
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.
Accepted to JFM Rapids, 11 pages, 6 figures
References in corpus (6)
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