Energy stability of plane Couette and Poiseuille flows and Couette paradox

Autor:	Falsaperla, Paolo, Mulone, Giuseppe, Perrone, Carla
Rok vydání:	2021
Předmět:	Physics - Fluid Dynamics Mathematical Physics 76E15 76E05 76D05
Druh dokumentu:	Working Paper
DOI:	10.1016/j.euromechflu.2022.01.006
Popis:	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. Comment: 22 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1807.07441
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.06443 Zobrazit plný text záznamu View this record from Arxiv