TY - JOUR
T1 - Steep Cliffs and Saturated Exponents in Three-Dimensional 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 Letter were performed using advanced computational facilities provided by the Texas Advanced Computation Center (TACC) under the XSEDE program supported by NSF. The data were generated using supercomputing resources at the Oak Ridge Leadership Computing Facility at the U.S. Department of Energy Oak Ridge National Laboratory. The work of J. S. was supported by the Tandon School of Engineering at New York University and Grant No. SCHU 1410/19-1 of the Deutsche Forschungsgemeinschaft. We thank Eric Siggia, Antonio Celani, Gregory Falkovich, Gregory Eyink, and Toshiyuki Gotoh for helpful comments.
Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/12/28
Y1 - 2018/12/28
N2 - The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a 40963 grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of 4/3.
AB - The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a 40963 grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of 4/3.
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U2 - 10.1103/PhysRevLett.121.264501
DO - 10.1103/PhysRevLett.121.264501
M3 - Article
C2 - 30636127
AN - SCOPUS:85059246235
SN - 0031-9007
VL - 121
JO - Physical Review Letters
JF - Physical Review Letters
IS - 26
M1 - 264501
ER -