Mach number study of supersonic turbulence: The properties of the density field

Abstract

We analyse the scaling properties of turbulent flows using a suite of three-dimensional numerical simulations. We model driven, compressible, isothermal, turbulence with Mach numbers ranging from the subsonic (ℳ ≈ 0.5) to the highly supersonic regime (ℳ ≈ 16). The forcing scheme consists of both solenoidal (transverse) and compressive (longitudinal) modes in equal parts. We confirm the relation σs2 = ln (1 + b2 ℳ2) between the Mach number and the standard deviation of the logarithmic density with b = 0.33. We find increasing deviations with higher Mach number from the predicted lognormal shape in the high-density wing of the density probability density function. The density spectra follow D{script}(k, ℳ) ∝ kζ(ℳ) with scaling exponents depending on the Mach number. We find ζ(ℳ) = αℳβ with coefficients α = -2.1 and β = -0.33. The dependence of the scaling exponent on the Mach number implies a fractal dimension D = 2 + 1.05 ℳ-0.33.