2025/02/17 by Chefranov, Sergey G., Chefranov, Alexander G.
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2503.00012
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.