Dissipative Structures in Supersonic Turbulence

Abstract

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. {\bf 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.