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Steady-State Bifurcation of a Non-parallel Flow Involving Energy Dissipation over a Hartmann Boundary Layer

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Zhi-Min Chen

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  1. Zhi-Min Chen
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Correspondence to Zhi-Min Chen.

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Communicated by Tim Healey.

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Chen, ZM. Steady-State Bifurcation of a Non-parallel Flow Involving Energy Dissipation over a Hartmann Boundary Layer. J Nonlinear Sci 31, 91 (2021). https://doi.org/10.1007/s00332-021-09752-y

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