Topological entropy of stationary three-dimensional turbulence

TL;DR

This paper introduces an Eulerian method to compute the topological entropy of stationary three-dimensional turbulence, enabling easier analysis of flow complexity without Lagrangian particle tracking.

Contribution

It extends previous work to 3D turbulence and provides an exact Eulerian framework based on local strain-rate eigenvalues and decorrelation times.

Findings

Provides a practical method using single-point measurements

Eliminates the need for complex Lagrangian tracking

Facilitates experimental analysis of flow mixing

Abstract

Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically necessitates a Lagrangian description. We extend our recent work [A. Manoharan, S. Subramanian, and A. Joy, Phys. Rev. E 112, 015106] to three dimensions, and present an exact Eulerian framework to compute the topological entropy of stationary turbulent flows. The only prerequisite is a distribution of eigenvalues of the local strain-rate tensor and their decorrelation times. This can be easily obtained from a single wire probe at a fixed location, thereby eliminating the need for Lagrangian particle tracking which is formidable due to the chaotic nature of the flow. We believe that our results lend great utility in experiments targeting transport and mixing in many industrial and natural flows.