Study of scalar gradient fields by geometric measure theory

Details Study of scalar gradient fields by geometric measure theory Study of scalar gradient fields by geometric measure theory

2004-01-12

arxiv.org/abs/nlin/0401015v1

Phys. Rev. E, 69 (2004) 047301

Nonlinear Sciences

Chaotic Dynamics

6 pages, 2 Postscript figures

Scientific paper

10.1103/PhysRevE.69.047301

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.

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