Abstract
We study the fractal scaling of iso-level sets of a passive scalar mixed by three-dimensional homogeneous and isotropic turbulence at high Reynolds numbers. The scalar field is maintained by a linear mean scalar gradient, and the Schmidt number is unity. A fractal box-counting dimension DF can be obtained for iso-levels below about three standard deviations of the scalar fluctuation on either side of its mean value. The dimension varies systematically with the iso-level, with a maximum of about 8/3 for the iso-level at the mean scalar value; this maximum dimension also follows as an upper bound from the geometric measure theory. We interpret this result to mean that mixing in turbulence is incomplete. A unique box-counting dimension for all iso-levels results when we consider the spatial support of the steep cliffs of the scalar conditioned on local strain rate; that unique dimension, independent of the iso-level set, is about 4/3.
Original language | English (US) |
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Article number | 044501 |
Journal | Physical Review Fluids |
Volume | 5 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2020 |
ASJC Scopus subject areas
- Computational Mechanics
- Modeling and Simulation
- Fluid Flow and Transfer Processes