Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations Academic Article uri icon


  • © 2016 Cambridge University Press. We report results from direct numerical simulation (DNS) of stationary compressible isotropic turbulence at very-high resolutions and a range of parameters using a massively parallel code at Taylor Reynolds numbers (Rλ) ranging from Rλ = 38 to 430 and turbulent Mach numbers (Mt) ranging from 0.1 to 0.6 on up to 20483 grid resolutions. A stationary state is maintained by a stochastic solenoidal forcing at the largest scales. The focus is on the mechanisms of energy exchanges, namely, dissipation, pressure-dilatation correlation and the individual contributing variables. Compressibility effects are studied by decomposing velocity and pressure fields into solenoidal and dilatational components. We suggest a critical turbulent Mach number at about 0.3 that separate two different flow regimes - only at Mach numbers above this critical value do we observe dilatational effects to affect the flow behaviour in a qualitative manner. The equipartition of energy between the dilatational components of kinetic and potential energy, originally proposed for decaying flows at low Mt, presents significant scatter at low Mt, but appears to be valid at high Mt for stationary flows, which is explained by the different role of dilatational pressure in decaying and stationary flows, and at low and high Mt. While at low Mt pressure possesses characteristics of solenoidal pressure, at high Mt it behaves in similar ways to dilatational pressure, which results in significant changes in the dynamics of energy exchanges. This also helps explain the observed qualitative change in the skewness of pressure at high Mt reported in the literature. Regions of high pressure are found to be correlated with regions of intense local expansions. In these regions, the density-temperature correlation is also seen to be relatively high. Classical scaling laws for low-order moments originally proposed for incompressible turbulence appear to be only weakly affected by compressibility for the range of Rλ and Mt investigated.

author list (cited authors)

  • Jagannathan, S., & Donzis, D. A.

citation count

  • 56

publication date

  • February 2016