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, $\gamma$ and $d$, based directly on their physical interpretations as the scaling exponent of the dissipation rate in the most intermittent structures ($\gamma$) and the dimension of the structures ($d$). We find that the best-fit parameters ($\gamma =0.71$ 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.

• Received 8 August 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.034501