Advection-Diffusion in Lagrangian Coordinates

Abstract

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.

6 pages, 2 postscript figures. LaTeX 2e with RevTeX 4 style. Final version

References in corpus (2)

• Structure of Small-Scale Magnetic Fields in the Kinematic Dynamo Theory
• Derivatives and Constraints in Chaotic Flows: Asymptotic Behaviour and a Numerical Method

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