Segment Description of Turbulence

TL;DR

This paper introduces a segment description method for turbulent solutions in evolution equations, aiming to provide an effective alternative to Reynolds averaging, with links to symbolic dynamics and shadowing techniques.

Contribution

It proposes a novel segment description approach for turbulence, connecting it with symbolic dynamics and shadowing, and highlights the challenge of numerical implementation.

Findings

Connects turbulence description with symbolic dynamics

Establishes a shadowing technique link

Highlights numerical implementation challenges

Abstract

We propose a segment description for turbulent solutions to evolution equations in an effort to develop an effective description rather than the classical Reynolds average. The new description has connections with symbolic dynamics and shadowing technique. The challenge of future study is how to effectively implement the description numerically.