Instability of the Kolmogorov flow in a wall-bounded domain

2019/02/24 by Chen, Zhi-Min
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.08916

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(10³). 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(10³). Further transition of the secondary flow is observed numerically. Especially, well developed turbulence arises at R=O(10⁴).

Related

• Zonostrophic instabilities in magnetohydrodynamic Kolmogorov flow
• The decay of wall-bounded MHD turbulence at low Rm
• Transition to turbulence in quasi-two-dimensional MHD flow driven by lateral walls
• Bifurcations of a plane parallel flow with Kolmogorov forcing
• Instability of the magnetohydrodynamics system at small but finite Reynolds number