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Study of scalar gradient fields by geometric measure theory

Joerg Schumacher
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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.

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Joerg Schumacher. 2004-01-12. Study of scalar gradient fields by geometric measure theory. https://doi.org/10.1103/physreve.69.047301

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