A two-layer description for some benchmark turbulent flows applicable to arbitrary values of the Reynolds number and the wall roughness

According to the existing theory, turbulent flow fields are divided into four layers, including (a) the viscous sublayer, (b) the buffer layer, (c) the logarithmic layer, and (d) the core layer. However, in this work, a two-layer description for some benchmark turbulent flows is proposed. To arrive at this description, firstly, the logarithmic layer is extended to include the buffer layer, which removes the need to consider the buffer layer with its complex formula. Thereafter, the attention is focused on some benchmark problems in fluid mechanics (i.e., the Couette flow, the 2D channel flow, the circular pipe flow, and the flow over a flat plate) and new descriptions are proposed for their core layers, incorporating the extended logarithmic layer. Hence, the accomplished two-layer description divides the considered turbulent flows into only (a) the viscous sublayer and (b) the extended core layer, each with a corresponding velocity profile. This description substantially simplifies the analysis and can be helpful for future studies. The proposed description is applicable to smooth as well as rough walls and is accurate for low, intermediate, and high Reynolds numbers. It is found that in spite of the simplicity of the proposed two-layer description, its outcomes in terms of the time-averaged velocity profile are in excellent agreement with those of previous studies, for all of the considered benchmark problems.