Scaling and Statistics in Three-Dimensional Compressible Turbulence

The scaling and statistical properties of three-dimensional compressible turbulence are studied using high-resolution numerical simulations and a heuristic model. The two-point statistics of the solenoidal component of the velocity field are found to be not significantly different from those of incompressible turbulence, while the scaling exponents of the velocity structure function for the compressive component become saturated at high orders. Both the simulated flow and the heuristic model reveal the presence of a power-law tail in the probability density function of negative velocity divergence (high compression regime). The power-law exponent is different from that in Burgers turbulence, and this difference is shown to have a major contribution from the pressure effect, which is absent in the Burgers turbulence.