2001/05/31 by Jean‐Luc Thiffeault, Jean-Luc Thiffeault · 34 citations
Computer Science · Mathematics · Physics and Astronomy · #Advection #Chaotic #Chaotic mixing #Classical mechanics #Convection–diffusion equation #Diffusion #Diffusion equation #Geometry #Lagrangian #Lagrangian and Eulerian specification of the flow field #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Quantum chaos and dynamical systems #Scalar (mathematics) #Square root #Thermal diffusivity #Vector field #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1016/s0375-9601(03)00244-5
published in Physics Letters A 309(5-6), 415-422 (Elsevier BV) · 6 pages, 2 postscript figures. LaTeX 2e with RevTeX 4 style. Final version
arxiv created 2003/01/27 · openalex publication_date 2003/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of dimensions, for a velocity field with chaotic trajectories, with an error proportional to the square root of the diffusivity. After some time, the one-dimensional equation becomes invalid, but by that time a large fraction of the scalar variance has decayed.