1. Energy stability of plane Couette and Poiseuille flows and Couette paradox
- Author
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Falsaperla, Paolo, Mulone, Giuseppe, and Perrone, Carla
- Subjects
Physics::Fluid Dynamics ,76E15, 76E05, 76D05 ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Physics - Fluid Dynamics ,Mathematical Physics - 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., 22 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1807.07441
- Published
- 2021