Emergence of universal scaling in isotropic turbulence

TL;DR

This study demonstrates that universal scaling laws in isotropic turbulence emerge at modest Reynolds numbers, with transverse velocity gradients showing higher intermittency than longitudinal ones, confirmed through high-resolution simulations.

Contribution

The paper provides numerical evidence that universal turbulence scaling appears at lower Reynolds numbers than previously thought, and highlights differences in intermittency between transverse and longitudinal velocity gradients.

Findings

Universal scaling occurs at Reynolds numbers around 10.

Transverse velocity gradients are more intermittent than longitudinal ones.

Scaling exponents are consistent with high Reynolds number inertial range predictions.

Abstract

Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power-laws in derivative statistics occurs at modest microscale Reynolds numbers of the order of 10, with the corresponding exponents being consistent with those for the inertial range structure functions at very high Reynolds numbers. In this paper we use well-resolved direct numerical simulations of homogeneous and isotropic turbulence to establish this result for a range of initial conditions with different forcing mechanisms. We also show that the moments of transverse velocity gradients possess larger scaling exponents than those of the longitudinal moments, confirming past results that the former are more intermittent than the latter.