Fluctuations of the Instantaneous Space Averages in Fragmentation with Kolmogorov Time Scales

TL;DR

This paper studies the time fluctuations of space averages in a turbulence fragmentation model with Kolmogorov scales, revealing strong temporal variability and the need for time averaging to reach steady states.

Contribution

It introduces a model combining fragmentation with Kolmogorov scales and analyzes the fluctuation behavior of space averages and PDFs in turbulence.

Findings

Space averages fluctuate strongly over time.

Time averaging is necessary to obtain steady-state distributions.

Fluctuations of PDFs exhibit unique intermittency properties.

Abstract

We investigate the time behavior of the fragmentation model with Kolmogorov time scales and space contraction resembling the random $\beta$-model of turbulence. The space averages computed at any instant using the entire spatial realization of the velocity field are shown to fluctuate strongly in time, and in this sense they are not observable. The time averaging required to achieve the steady-state distributions in the case of constant energy supply are found. The fluctuations of the probability distribution functions (PDFs) have intermittency properties different from those of PDFs.