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Communication Dans Un Congrès Année : 2007

Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D 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 Poisseuille flow, this problem is frequently cited as a paradigm for transition to turbulence. Our approach consists in generating an exact trajectory of the nonlinear system that approaches exponentially the objective profile. A boundary control law guarantees then that the error between the state and the trajectory decays exponentially in the $L^2$ norm. The result is first proved for the linearized Stokes equations, then shown to hold for the nonlinear Navier Stokes system.
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Dates et versions

hal-00086480 , version 1 (18-07-2006)

Identifiants

  • HAL Id : hal-00086480 , version 1

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Jean-Michel Coron, Emmanuel Trélat, Rafael Vazquez. Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D Channel Flow. CTS-HYCON Workshop, 2006, Paris, France. pp.699--720. ⟨hal-00086480⟩
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