Universality and anisotropy in passive scalar fluctuations in turbulence with uniform mean gradient

Abstract

Passive scalar and velocity fluctuations in homogeneous isotropic turbulence with or without mean scalar gradient are studied by using high-resolution direct numerical simulation (DNS). The local scaling exponents of the velocity structure functions are newly computed at larger Reynolds number, and the values at their plateau in the inertial range are found to be consistent with the previous DNS and experimental data. The 4/3 law for the velocity–scalar mixed correlation and the high-order structure functions of the passive scalar increment are analyzed in terms of the Legendre polynomial expansion. It is shown theoretically that the contributions from the second order in the expansion can be removed by taking the average over three directions parallel and perpendicular to the mean gradient, and it is found numerically that the contributions higher than the fourth order are negligible. The scaling exponents of the isotropic part of the scalar structure functions under the mean gradient are found to have the well-developed scaling range and are smaller than those in the isotropic case. The different behavior in the local scaling exponents with or without the mean gradient is examined and the universality of the scaling exponents is discussed.

Keywords:

• turbulence
• passive scalar
• scaling exponent
• universality
• anisotropy

Acknowledgments

The authors thank Profs. Hill and Kaneda for their valuable discussions, and the Theory and Computer Simulation Center of the National Institute for Fusion Science (NIFS10KNSS008), and JHPCN and HPC at the Information Technology Center of Nagoya University for providing the computational resources. T.G. and T.W.’s work were partially supported by Grant-in-Aid for Scientific Research No. 21360082 and No. 23760156, respectively, from the Ministry of Education, Culture, Sports, Science and Technology of Japan. T.G was also supported in part by the National Science Foundation under Grant No. PHY05-51164 within the program “The nature of Turbulence”, held at the Kavli Institute of Theoretical Physics at the University of California, Santa Barbara, CA.