TY - JOUR

T1 - Scaling exponents saturate in three-dimensional isotropic turbulence

AU - Iyer, Kartik P.

AU - Sreenivasan, Katepalli R.

AU - Yeung, P. K.

N1 - Funding Information:
We are grateful to many of our colleagues with whom we discussed these results over the years, in one form or another, and to Xiaomeng Zhai and Matthew Clay for their participation in the computations. This work was partially supported by the National Science Foundation (NSF), via Grants No. ACI-1640771 and No. ACI-1036170 at the Georgia Institute of Technology. The computations were performed using supercomputing resources provided through the XSEDE consortium (which is funded by NSF) at the Texas Advanced Computing Center at the University of Texas (Austin), and the Blue Waters Project at the National Center for Supercomputing Applications at the University of Illinois (Urbana-Champaign).
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/5

Y1 - 2020/5

N2 - From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the following (somewhat contested) results: the 4/5ths law holds in an intermediate range of scales and that the second-order exponent over the same range of scales is anomalous, departing from the self-similar value of 2/3 and approaching a constant of 0.72 at high Reynolds numbers. We compare to some typical theories the dependence of longitudinal exponents as well as their derivatives with respect to the moment order n, and estimate the most probable value of the Hölder exponent. We demonstrate that the transverse scaling exponents saturate for large n, and trace this trend to the presence of large localized jumps in the signal. The saturation value of about 2 at the highest Reynolds number suggests, when interpreted in the spirit of fractals, the presence of vortex sheets rather than more complex singularities. In general, the scaling concept in hydrodynamic turbulence appears to be more complex than even the multifractal description.

AB - From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the following (somewhat contested) results: the 4/5ths law holds in an intermediate range of scales and that the second-order exponent over the same range of scales is anomalous, departing from the self-similar value of 2/3 and approaching a constant of 0.72 at high Reynolds numbers. We compare to some typical theories the dependence of longitudinal exponents as well as their derivatives with respect to the moment order n, and estimate the most probable value of the Hölder exponent. We demonstrate that the transverse scaling exponents saturate for large n, and trace this trend to the presence of large localized jumps in the signal. The saturation value of about 2 at the highest Reynolds number suggests, when interpreted in the spirit of fractals, the presence of vortex sheets rather than more complex singularities. In general, the scaling concept in hydrodynamic turbulence appears to be more complex than even the multifractal description.

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U2 - 10.1103/PhysRevFluids.5.054605

DO - 10.1103/PhysRevFluids.5.054605

M3 - Article

AN - SCOPUS:85087898087

SN - 2469-990X

VL - 5

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 5

M1 - 054605

ER -