title: Scalar gradient fields by geometric measure theory.
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< or =Sc< or =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.
authors.affiliation: Fachbereich Physik, Philipps-Universität, D-35032 Marburg, Germany.
authors.forename: Jörg
authors.initials: J
authors.lastname: Schumacher