We will study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L-2-energy. We will prove that the streamwise perturbations are L-2-energy stable for any Reynolds number. This contradicts the results of Joseph (1966), Joseph and Carmi (1969) and Busse (1972), and allows us to prove, with a conjecture, that the critical nonlinear Reynolds numbers are obtained along two-dimensional perturbations, the spanwise perturbations, as Orr (1907) had supposed. This conclusion combined with some recent results by Falsaperla et al. (2019) on the stability with respect to tilted rolls, provides a possible solution to the "mismatch " between the critical values of linear stability, nonlinear monotonic energy stability and the experiments. (c) 2022 Elsevier Masson SAS. All rights reserved.

Energy stability of plane Couette and Poiseuille flows: A conjecture

Paolo Falsaperla;Giuseppe Mulone
;
Carla Perrone
2022-01-01

Abstract

We will study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L-2-energy. We will prove that the streamwise perturbations are L-2-energy stable for any Reynolds number. This contradicts the results of Joseph (1966), Joseph and Carmi (1969) and Busse (1972), and allows us to prove, with a conjecture, that the critical nonlinear Reynolds numbers are obtained along two-dimensional perturbations, the spanwise perturbations, as Orr (1907) had supposed. This conclusion combined with some recent results by Falsaperla et al. (2019) on the stability with respect to tilted rolls, provides a possible solution to the "mismatch " between the critical values of linear stability, nonlinear monotonic energy stability and the experiments. (c) 2022 Elsevier Masson SAS. All rights reserved.
Plane Couette
Plane Poiseuille
Nonlinear energy stability
Weighted energy
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/542962
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