Near-wall turbulent transport of large-Schmidt-number passive scalars

Turbulent diffusion of a passive scalar with a large-Schmidt number (Sc >> 1) is considered in the viscous sublayer of a turbulent channel flow. Close to the wall, the corresponding eddy diffusivity coefficient is expanded as a power series in terms of the viscous distance to the wall y . The coefficients of the series depend on the Schmidt number and the analysis of recent numerical results allows to conclude that in the close vicinity of the wall (y << Sc(-1/3)) , the y(3) term is the dominant term; whereas, at distances relatively large from the wall (Sc(-1/3)<< y <<1) , the y(4) term becomes dominant. Accordingly, in this region the turbulent Schmidt number is not constant but follows a hyperbolic law in terms of the distance to the wall that matches the values taken in the vicinity of the wall, on the order of Sc(-1/3) , with the values of order unity in the rest of the viscous layer. The implications of this behavior on the surface-transfer coefficient are analyzed.