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.