Study of scalar gradient fields by geometric measure theory
Chaotic Dynamics
2009-11-10 v1 Fluid Dynamics
Abstract
Upper bounds of the Hausdorff volume of scalar gradient field graphs are derived by means of geometric measure theory. The approach reproduces that scalar gradient fields along a mean imposed scalar gradient become space filling for sufficiently high values of Schmidt numbers Sc. The bounds are consistent with findings from recent high-resolution numerical experiments for 1<= Sc <= 64, but too rough when compared with numerical simulations. A Reynolds number dependence of the bounds is found due to the additional scalar gradient stretching term in the equation of motion.
Cite
@article{arxiv.nlin/0401015,
title = {Study of scalar gradient fields by geometric measure theory},
author = {Joerg Schumacher},
journal= {arXiv preprint arXiv:nlin/0401015},
year = {2009}
}
Comments
6 pages, 2 Postscript figures