Instabilities and mixing in two-dimensional Kolmogorov flow

TL;DR

This paper investigates how transitions and subtle changes in two-dimensional Kolmogorov flow affect flow stability and mixing, revealing that minor flow variations can significantly impact transport properties due to resonance interactions.

Contribution

It provides a theoretical analysis linking flow instabilities and resonance interactions to mixing behavior in 2D Kolmogorov flow, highlighting non-intuitive effects.

Findings

Significant flow changes do not always alter transport properties.

Subtle flow modifications can dramatically change mixing.

Resonance interactions explain paradoxical mixing behaviors.

Abstract

This paper presents results of a theoretical investigation of transport in a numerical model of a two-dimensional Kolmogorov flow. We investigate the changes in its mixing properties associated with transition from laminar regime to turbulence. It is found that significant changes in the flow do not always lead to comparable changes in its transport properties. On the other hand, some very subtle changes in the flow can dramatically alter the degree of mixing. We show that interaction of multiple resonances can provide an explanation for many of these seemingly paradoxical results.