Scaling properties of the equation for passive scalar transport in wall-bounded turbulent flows

Data from direct numerical simulations (DNS) of fully-developed turbulent channel flows subjected to a constant surface heat-flux are used to explore the scaling behaviours admitted by the mean thermal energy equation. Following the framework of Wei et al. (2005) [1,2], the analysis employs a theory based on the magnitude ordering of terms in the mean thermal energy equation of wall-bounded turbulent heat transfer. A four layer thermal structure has been identified from the leading order terms in the mean energy equation. A review of the limitations of traditional and existing scaling of mean temperature and turbulent heat flux is conducted. The possibilities of a new scaling approach with the introduction of generalized thermal length scale are discussed within the context of the four-layer framework. This methodology generally seeks to determine the invariant form(s) admitted by the relevant equation. Investigation of normalized statistical quantities applicable to inner, outer and intermediate regions of the flow, whose properties are dependent on a small parameter that is a function of either Reynolds number or both Reynolds and Prandtl numbers, shows inconsistencies between the normalizations on the different subdomains. Although the present scaling approach successfully explores the generalized properties of intermediate layer, issues pertaining to simultaneously and self-consistently reconciling the inner and intermediate normalizations remain unresolved.