Intermittency and scaling of passive scalar convected by isotropic steady turbulence under the uniform mean scalar gradient
Seminar Room 1, Newton Institute
It has been more convincing that passive scalar in turbulence is more intermittent than the turbulent velocity field itself, implying that the small scales of the passive scalar are more affected by the large scale conditions. In order to get more precise knowledge about the scaling behavior of the passive scalar for various Reynolds (Peclet) numbers and large scale conditions, we have performed very high resolution direct numerical simulations (DNSs) of the passive scalar turbulence with or without uniform mean scalar gradient up to $2048^3$ grid points and $R_\lambda\approx 600$, and analysed the various statistical functions. Turbulent velocity field was statistically in a steady and isotropic state by Gaussian random force applied at large scales. Fundamental statistics such as the spectra of the kinentic energy, pressure, scalar variance, scalar-velocity flux were examined, especially in their scaling behavior.
It is found that although curves of the kinetic energy and scalar spectra are well collapsed onto a single curve when the Kolmogorov variables are used, while the others are not as well as the former, suggesting need of more elaborated scaling. The scaling of the velocity structure functions is consistent with the existing data of experiments and DNSs, while the scaling of the passive scalar is not convincing and difficult to reach definite conclusion. When the isotropic random injection for the passive scalar is applied at large scales (Case R), each curve of the local scaling exponent at a given order has one local minimum and maximum point, unlike the velocity case, and plateau is not wide enough to precisely determine the scaling exponents. On the other hand, when the uniform mean scalar gradient is applied (Case G), the curves of the local scaling exponents of the isotropic sector are found to have well developed plateau, and their plateau levels are smaller than those of Case R, meaning stronger intermittency for the Case of G. Crossover of the velocity and scalar structure functions is also examined. The crossover of the transverse velocity structure functions is found to be very similar to that of the passive scalar. We seek the reason for the above differences and similarities.