A model for passive scalar transport in turbulent channel flow

Passive scalar in turbulent boundary layer is transported via the momentum field, which at high Reynolds number is composed of large uniform momentum zones (UMZs) segregated by narrow regions of concentrated vorticity. Recent experimental studies indicate the scalar field is also composed of large uniform scalar zones (USZs) segregated by narrow regions of concentrated scalar gradient.

A model that reproduces the fundamental elements of the USZ structure by placing a few concentrated regions of scalar gradient across the boundary layer is presented. The number of concentrated regions of scalar gradient, their most probable location and corresponding scalar quantity in the outer region of the scalar boundary layer (in which the molecular diffusion is negligible) is developed by the analysis of the mean scalar transport equation. An asymptotic length and scalar scaling in the inner region of the boundary layer is explored. Moreover, the combined effects of Re and Pr numbers on the USZ structure is investigated. The numerical results show the model can reproduce the main characteristics of the scalar field up to the fourth statistical moment. Furthermore, in conjugation with the UMZ model developed by the authors, the mode can produce the streamwise velocity-scalar correlation.