Is the Scaling of Supersonic Turbulence Universal?

TL;DR

This paper investigates whether the statistical properties of supersonic turbulence are universal at small scales, finding that traditional velocity statistics are not, but a reformulated approach reveals near-universal scaling laws linked to shock structures.

Contribution

The study introduces a reformulation of the refined similarity hypothesis using mass-weighted velocity, demonstrating near-universal scaling laws in supersonic turbulence despite different forcing conditions.

Findings

Velocity statistics are not universal in supersonic turbulence.

Reformulated scaling laws are insensitive to external forcing.

Intermittent structures are shocks following Burgers turbulence scaling.

Abstract

The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of supersonic turbulent flow driven by external forcing, we demonstrate that this is not generally true for the two-point velocity statistics of compressible turbulence. However, a reformulation of the refined similarity hypothesis in terms of the mass-weighted velocity rho^(1/3)v yields scaling laws that are almost insensitive to the forcing. The results imply that the most intermittent dissipative structures are shocks closely following the scaling of Burgers turbulence.