Work

Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D Channel Flow

Year: 2006

Type: conference-paper

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 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.

Source: HAL

Authors: Coron, Jean-Michel, Trélat, Emmanuel, Vazquez, Rafael

Institutions: Laboratoire de Mathématiques d'Orsay, Laboratoire de Mathématiques Analyse, Probabilités, Modélisation Orléans, University of California System

Language: English

Topic: Fluid Dynamics and Turbulent Flows

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4321274580

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