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arXiv · 2105.00742

Bifurcating steady-state flows involving energy dissipation over a Hartmann boundary layer

Zhi-Min Chen
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Abstract

A plane non-parallel vortex flow in a square fluid domain is examined. The energy dissipation of the flow is dominated by viscosity and linear friction effect of a Hartmann layer. This is a traditional Navier-Stokes flow when the linear friction effect is not involved, whereas it is a magnetohydrodynamic flow when the energy dissipation is fundamentally dominated by the friction. It is proved that linear critical values of a spectral problem are nonlinear thresholds leading to the onset of secondary steady-state flows, the nonlinear phenomenon observed in laboratory experiments.

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Zhi-Min Chen. 2021-09-26. Bifurcating steady-state flows involving energy dissipation over a Hartmann boundary layer. https://doi.org/10.1007/s00332-021-09752-y

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