English

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

Analysis of PDEs 2021-09-28 v2

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.

Keywords

Cite

@article{arxiv.2105.00742,
  title  = {Bifurcating steady-state flows involving energy dissipation over a Hartmann boundary layer},
  author = {Zhi-Min Chen},
  journal= {arXiv preprint arXiv:2105.00742},
  year   = {2021}
}