Alexei G. Kritsuk, Rick Wagner, Michael L. Norman
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 (2011) Phys. Rev. Lett. 107, 134501]. Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogs 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.
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http://arxiv.org/abs/1306.5768
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