# Intermittent direction reversals of moving spatially-localized turbulence observed in two-dimensional Kolmogorov flow

## TL;DR

This study observes that in two-dimensional Kolmogorov flow, a localized turbulence can stably move and randomly switch directions, with internal turbulence dynamics influencing its intermittent reversals.

## Contribution

It reveals that the direction switching of localized turbulence is governed by internal turbulent dynamics and introduces a coarse-grained analysis to separate motion from internal turbulence.

## Key findings

- Localized turbulence travels with constant speed
- Direction switching appears as a random telegraph signal
- Internal turbulence asymmetry correlates with switching behavior

## Abstract

We have found that in two-dimensional Kolmogorov flow a single spatially-localized turbulence (SLT) exists stably and travels with a constant speed on average switching the moving direction randomly and intermittently for moderate values of control parameters: Reynolds number and the flow rate. We define the coarse-grained position and velocity of an SLT and separate the motion of the SLT from its internal turbulent dynamics by introducing a co-moving frame. The switching process of an SLT represented by the coarse-grained velocity seems to be a random telegraph signal. Focusing on the asymmetry of the internal turbulence we introduce two coarse-grained variables characterizing the internal dynamics. These quantities follow the switching process reasonably. This suggests that the twin attracting invariant sets each of which corresponds to a one-way traveling SLT are embedded in the attractor of the moving SLT and the connection of the two sets is too complicated to be represented by a few degrees of freedom but the motion of an SLT is controlled by the internal turbulent dynamics.