Rescaling the near-wall predictive model for passive scalars in turbulent channel flow

Abstract

The predictive model for near-wall velocity fluctuations [I. Marusic, R. Mathis, and N. Hutchins, “Predictive model for wall-bounded turbulent flow,” Science 329, 193–196 (2010)] is also valid for passive scalars transported in wall-bounded turbulent flows. However, the model parameters show strong Prandtl number (Pr) dependence under the viscous scaling. In the present study, we introduced the Prandtl-number-dependent length unit to scale the model parameters. Under the proposed scaling, the wall-normal positions of the outer peak of the scalar spectra coincide with 4.5ReτPr, where Reτ is the friction Reynolds number. With the large-scale signals extracted at this position as the model input, the Prandtl number dependence of the model parameters is greatly weakened, and the wall-normal position of zero modulation is independent of Prandtl numbers.