Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence

TL;DR

This paper investigates the distribution of local dissipation scales in fluid turbulence, revealing how these scales vary with Reynolds number and confirming theoretical predictions through high-resolution simulations.

Contribution

It introduces a detailed analysis of local dissipation scales in turbulence, extending the understanding beyond the mean dissipation length with unprecedented spectral resolution.

Findings

Distribution of local dissipation scales matches theoretical predictions.

Higher Reynolds numbers generate finer local dissipation scales.

Energy spectrum lacks a bottleneck at high Reynolds numbers.

Abstract

We relate the intermittent fluctuations of velocity gradients in turbulence to a whole range of local dissipation scales generalizing the picture of a single mean dissipation length. The statistical distribution of these local dissipation scales as a function of Reynolds number is determined in numerical simulations of forced homogeneous isotropic turbulence with a spectral resolution never applied before which exceeds the standard one by at least a factor of eight. The core of the scale distribution agrees well with a theoretical prediction. Increasing Reynolds number causes the generation of ever finer local dissipation scales. This is in line with a less steep decay of the large-wavenumber energy spectra in the dissipation range. The energy spectrum for the highest accessible Taylor microscale Reynolds number R_lambda=107 does not show a bottleneck.