Study of scalar gradient fields by geometric measure theory
arXiv:nlin/0401015 · doi:10.1103/PhysRevE.69.047301
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.
arXiv comment6 pages, 2 Postscript figures
References in corpus (5)
- On statistically stationary homogeneous shear turbulence
- Geometric features of the mixing of passive scalars at high Schmidt numbers
- Derivative moments in stationary homogeneous shear turbulence
- Fractal dimension crossovers in turbulent passive scalar signals
- Structure function of passive scalars in two-dimensional turbulence