Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations

TL;DR

This paper investigates the kinetic energy spectrum in the dissipative range of turbulence, using experiments and simulations, and finds it follows a stretched exponential with an exponent matching theoretical predictions.

Contribution

The study provides the first precise estimate of the stretched exponential exponent in the near-dissipative range, confirming the theoretical value of 2/3.

Findings

Spectra follow a stretched exponential with exponent ~0.68.

Results agree with the theoretical prediction of 2/3 for the exponent.

Experimental and numerical data are consistent in the near-dissipative range.

Abstract

We present a statistical analysis of the behavior of the kinetic energy spectrum in the dissipative range of scales of fully developed three-dimensional turbulence. We analyze spectra recorded in experiments of grid turbulence generated in the Modane wind tunnel, and spectra obtained from high-resolution direct numerical simulations of the forced Navier-Stokes equation. We focus on wave-number scales in the near-dissipative range. We find that in this domain, the spectra behave as a stretched exponential with an exponent $\alpha = 0.68 \pm 0.19$. This result corroborates previous DNS studies which found that the spectrum in the near-dissipative range is best modeled by a stretched exponential with $\alpha<1$. Moreover, we here give an estimate for the actual value of $\alpha$, which turns out to be in precise agreement with the theoretical prediction $\alpha=2/3$ from the non-perturbative renormalisation group.