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arXiv · 1902.08916

Instability of the Kolmogorov flow in a wall-bounded domain

Zhi-Min Chen
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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 $R=O(10^4)$.

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Zhi-Min Chen. 2019-02-24. Instability of the Kolmogorov flow in a wall-bounded domain. https://arxiv.org/abs/1902.08916

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