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arXiv · 2503.00012

Revision of the linear stability paradox for known bounded shear flows

Sergey G. Chefranov·Alexander G. Chefranov
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Abstract

The well-known paradox of linear stability for the some bounded shear flows is not solved up to now and is bypassed on the basis of the non-linear mechanisms consideration. We prove that it is arising only due to an idealized assumption of an exact space periodicity for the small hydrodynamic perturbations. When finite non-zero viscosity is taken into account only quasi-periodic boundary conditions must be used. The conditions of linear instability to the Hagen-Poiseuille flow and to the plane Couette flow are obtained.

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Sergey G. Chefranov, Alexander G. Chefranov. 2025-02-17. Revision of the linear stability paradox for known bounded shear flows. https://arxiv.org/abs/2503.00012

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