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arXiv · 2105.06443

Energy stability of plane Couette and Poiseuille flows and Couette paradox

Paolo Falsaperla·Giuseppe Mulone·Carla Perrone
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Abstract

We study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L2-energy. We prove that the streamwise perturbations are L2-energy stable for any Reynolds number. This contradicts the results of Joseph [10], Joseph and Carmi [12] and Busse [4], and allows us to prove that the critical nonlinear Reynolds numbers are obtained along two-dimensional perturbations, the spanwise perturbations, as Orr [16] had supposed. This conclusion combined with recent results by Falsaperla et al. [8] on the stability with respect to tilted rolls, provides a possible solution to the Couette-Sommerfeld paradox.

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Paolo Falsaperla, Giuseppe Mulone, Carla Perrone. 2021-05-13. Energy stability of plane Couette and Poiseuille flows and Couette paradox. https://doi.org/10.1016/j.euromechflu.2022.01.006

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