Control for Fast and Stable Laminar-to-High-Reynolds-Numbers Transfer in a 2D Navier-Stokes Channel Flow - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2008

Control for Fast and Stable Laminar-to-High-Reynolds-Numbers Transfer in a 2D Navier-Stokes Channel Flow

Résumé

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 $L^2$, $H^1$, and $H^2$ norms. The result is first proved for the linearized Stokes equations, then shown to hold locally for the nonlinear Navier-Stokes system.
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Dates et versions

hal-00131057 , version 1 (15-02-2007)
hal-00131057 , version 2 (24-08-2008)

Identifiants

  • HAL Id : hal-00131057 , version 2

Citer

Rafael Vazquez, Emmanuel Trélat, Jean-Michel Coron. 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, 2008, 10 (4), pp.925--956. ⟨hal-00131057v2⟩
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