Dissipative Structures in Supersonic Turbulence

TL;DR

This paper demonstrates that the She and Lévéque model accurately describes the density-weighted moments of dissipation rates in supersonic turbulence, providing a method to measure key model parameters directly from physical interpretations.

Contribution

It introduces a general method to measure the She and Lévéque model parameters, $b3$ and $d$, from physical interpretations, and confirms the model's validity in high Mach number turbulence.

Findings

The model fits well with simulation data at Mach 6.

Measured parameters $b3=0.71$ and $d=1.90$ agree with direct measurements.

Validates the She and Lévéque model for supersonic turbulence.

Abstract

We show that density-weighted moments of the dissipation rate, $\epsilon_l$, averaged over a scale $l$, in supersonic turbulence can be successfully explained by the She and L\'ev\^eque model [Phys. Rev. Lett. {\bf 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 $\epsilon_l$ scalings in a simulation of supersonic turbulence at Mach 6 agree with their direct measurements, confirming the validity of the model in supersonic turbulence.