Advection-Diffusion in Lagrangian Coordinates
混沌动力学
2009-11-07 v5 流体动力学
摘要
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.
引用
@article{arxiv.nlin/0105026,
title = {Advection-Diffusion in Lagrangian Coordinates},
author = {Jean-Luc Thiffeault},
journal= {arXiv preprint arXiv:nlin/0105026},
year = {2009}
}
备注
6 pages, 2 postscript figures. LaTeX 2e with RevTeX 4 style. Final version