On the relationship between the roughness length of a scalar quantity and the corresponding sublayer-Stanton number

Abstract

Considering Sheppard's effective diffusivity approach for the molecular-turbulent sublayer, the relationship between the roughness length of a scalar quantity, zp and the corresponding sublayer-Stanton number, Bi, ist re-formulated. This re-formulation leads to Bi-1 = k-1 ln (1+zo/zp), where zo is the roughness length for momentum. Based on this equation, it is evident that (a) the relationship Bi-1 = k-1 ln (1+zo/zp commonly used is a doubtful approximation for the interfacial sublayer, and (b) the sublayer-Stanton number is positive-definite even if zp≥zo > 0. This is in contrast to negative Bi-1 values found in the literature. Moreover, it is shown that Bi-1 values derived with Sheppard's approach are much smaller than those provided by the more adequate Reichardt's approach.

Keywords

• molecular-turbulent sublayer
• diffusionskoeffizient