2008/03/05 by Emmanuelle Gouillart, Olivier Dauchot, B. Dubrulle +4
Computer Science · Mathematics · Physics and Astronomy · #Advection #Algebraic number #Bifurcation #Chaotic #Chaotic mixing #Classical mechanics #Exponential decay #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Mechanics #Mixing (physics) #Nonlinear Dynamics and Pattern Formation #Normal mode #Observable #Phase space #Physics #Poincaré map #Quantum chaos and dynamical systems #Quantum mechanics #Slip (aerodynamics) #Theoretical and Computational Physics #Vibration #cond-mat.soft
paper · pdf · doi:10.1103/physreve.78.026211
published as Phys. Rev. E 78, 026211 (2008) · 17 pages, 12 figures
arxiv created 2008/03/05 · openalex publication_date 2008/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Chaotic mixing in a closed vessel is studied experimentally and numerically in different two-dimensional (2D) flow configurations. For a purely hyperbolic phase space, it is well known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincaré section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.