English

Instability of the Kolmogorov flow in a wall-bounded domain

Analysis of PDEs 2019-02-26 v1

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)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(103)R=O(10^3). Further transition of the secondary flow is observed numerically. Especially, well developed turbulence arises at R=O(104)R=O(10^4).

Keywords

Cite

@article{arxiv.1902.08916,
  title  = {Instability of the Kolmogorov flow in a wall-bounded domain},
  author = {Zhi-Min Chen},
  journal= {arXiv preprint arXiv:1902.08916},
  year   = {2019}
}