Article
Control for fast and stable laminar-to-high-Reynolds-numbers transfer in a 2D Navier-Stokes channel flow
Author/s | Vázquez Valenzuela, Rafael
Trélat, Emmanuel Coron, Jean Michel |
Department | Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos |
Publication Date | 2008 |
Deposit Date | 2021-06-08 |
Published in |
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Abstract | We consider the problem of generating and tracking a trajectory
between two arbitrary parabolic profiles of a periodic 2D channel flow, which
is linearly unstable for high Reynolds numbers. Also known as the Poiseuille
flow, ... We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also known as the Poiseuille flow, this problem is frequently cited as a paradigm for transition to turbulence. Our procedure consists in generating an exact trajectory of the nonlinear system that approaches exponentially the objective profile. Using a backstepping method, we then design boundary control laws guaranteeing that the error between the state and the trajectory decays exponentially in L2 , H1 , and H2 norms. The result is first proved for the linearized Stokes equations, then shown to hold locally for the nonlinear Navier-Stokes system. |
Citation | Vázquez Valenzuela, R., Trélat, E. y Coron, J.M. (2008). Control for fast and stable laminar-to-high-Reynolds-numbers transfer in a 2D Navier-Stokes channel flow. Discrete and Continuous Dynamical Systems. Series B, 10 (4), 925-956. |
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