Monotone shear flows that are either nearly linear or have no inflection point are linearly stable in the large Reynolds limit, in a periodic channel with no-slip or traction boundary conditions.
Linear stability of pipe Poiseuille flow at high Reynolds number regime
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abstract
In this paper, we prove the linear stability of the pipe Poiseuille flow for general perturbations at high Reynolds number regime. This is a long-standing problem since the experiments of Reynolds in 1883. Our work lays a foundation for the theoretical analysis of hydrodynamic stability of pipe flow, which is one of the oldest yet unsolved problems of fundamental fluid dynamics.
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On the stability of laminar flows between plates
Monotone shear flows that are either nearly linear or have no inflection point are linearly stable in the large Reynolds limit, in a periodic channel with no-slip or traction boundary conditions.