TY - JOUR
T1 - Fractal iso-level sets in high-Reynolds-number scalar turbulence
AU - Iyer, Kartik P.
AU - Schumacher, Jörg
AU - Sreenivasan, Katepalli R.
AU - Yeung, P. K.
N1 - Funding Information:
The computations and data analyses reported in this paper were performed using advanced computational facilities provided by the Texas Advanced Computation Center (TACC) under the XSEDE program supported by the US National Science Foundation under Grant No. ACI-1036170. The data sets used were originally generated using supercomputing resources at the Oak Ridge Leadership Computing Facility at the US Department of Energy Office of Science user facility supported under Contract No. DE-AC05-00OR22725 Oak Ridge National Laboratory. We thank Dr. Inigo San Gil for his involvement 20 years ago in this project using low-resolution data, Prof. Diego Donzis for his initiative on the high-resolution passive scalar simulations reported here, and Prof. Charles Meneveau for useful comments. J.S. wishes to thank the Tandon School of Engineering at New York University for financial support.
Publisher Copyright:
© 2020 American Physical Society. ©2020 American Physical Society.
PY - 2020/4
Y1 - 2020/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85084966798&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85084966798&partnerID=8YFLogxK
U2 - 10.1103/PhysRevFluids.5.044501
DO - 10.1103/PhysRevFluids.5.044501
M3 - Article
AN - SCOPUS:85084966798
SN - 2469-990X
VL - 5
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 4
M1 - 044501
ER -