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arXiv · 2404.07065

Hopf bifurcation of a non-parallel Navier-Stokes flow

Zhi-Min Chen
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Abstract

A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf bifurcation or secondary time periodic flows branching of a basic square eddy flow is found. In contrast to a square eddy flow involving an even number of vortices in earlier analytical and experimental investigations, instability of the flow leads to steady-state bifurcations.

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Zhi-Min Chen. 2024-04-10. Hopf bifurcation of a non-parallel Navier-Stokes flow. https://arxiv.org/abs/2404.07065

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