On the large-scale sweeping of small-scale eddies in turbulence -- A filtering approach

TL;DR

This paper uses a filtering technique to analyze the multi-scale structure of turbulence, providing bounds and confirming predictions with simulations to improve understanding of large-scale equations in turbulent flows.

Contribution

It introduces a filtering approach to analyze small-scale eddies in turbulence and establishes rigorous bounds, validated by numerical simulations.

Findings

Validated analytical bounds with numerical data

Provided insights into multi-scale interactions in turbulence

Discussed implications for large-scale turbulence modeling

Abstract

We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by larger scales is considered, and rigorous upper bounds are established for the various dynamically active scales. The analytical predictions are confirmed with direct numerical simulation data. The results are discussed with respect to the establishment of effective large-scale equations valid for turbulent flows.