# Instability of the Kolmogorov flow in a wall-bounded domain

## TL;DR

This paper investigates the stability and transition of Kolmogorov flow in a wall-bounded domain within magnetohydrodynamics, confirming experimental observations and exploring turbulence onset at high Reynolds numbers.

## Contribution

The study proves the existence of a secondary steady state flow in wall-bounded MHD Kolmogorov flow and aligns theoretical solutions with experimental data.

## Key findings

- Secondary steady state flow exists at R=O(10^3)
- Theoretical solutions agree with laboratory measurements
- Turbulence develops at R=O(10^4)

## Abstract

In the magnetohydrodynamics (MHD) experiment performed by Bondarenko and his co-workers in 1979, the Kolmogorov flow loses stability and transits into a secondary steady state flow at the Reynolds number $R=O(10^3)$. This problem is modelled as a MHD flow bounded between lateral walls under slip wall boundary condition. The existence of the secondary steady state flow is now proved. The theoretical solution has a very good agreement with the flow measured in laboratory experiment at $R=O(10^3)$. Further transition of the secondary flow is observed numerically. Especially, well developed turbulence arises at $R=O(10^4)$.