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Unstable manifolds computation for the 2-D plane Poiseuille flow
Sánchez Casas, José Pablo; Jorba, Angel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We follow the unstable manifold of periodic and quasi-periodic solutions for the Poiseuille problem, using two formulations: holding constant flux or mean pressure gradient. By means of a numerical integrator of the Navier-Stokes equations, we let the fluid evolve from a perturbed unstable solution. We detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with 2 or 3 basic frequencies and more complex sets that we have not been able to classify.
Differentiable dynamical systems
Fluid mechanics
Poiseuille flow
unstable manifolds
Sistemes dinàmics diferenciables
Teoria ergòdica
Fluids
Vorticitat -- Teoria
Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications
Classificació AMS::76 Fluid mechanics::76D Incompressible viscous fluids
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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