Dissipative Structures in Supersonic Turbulence

We show that density-weighted moments of the dissipation rate, ϵ_l, averaged over a scale l, in supersonic turbulence can be successfully explained by the She and Lévêque model [ Phys. Rev. Lett. 72 336 (1994)]. A general method is developed to measure the two parameters of the model, γ and d, based directly on their physical interpretations as the scaling exponent of the dissipation rate in the most intermittent structures (γ) and the dimension of the structures (d). We find that the best-fit parameters (γ=0.71 and d=1.90) derived from the ϵ_l scalings in a simulation of supersonic turbulence at Mach 6 agree with their direct measurements, confirming the validity of the model in supersonic turbulence.