Scaling and modeling of three-dimensional, pressure-driven turbulent boundary layers

An asymptotic analysis of three-dimensional, pressure-driven, turbulent boundary layers is presented. Equations of mass conservation, momentum, and for expansions occurring in outer, middle, and inner layers are defined. The flow is analytically demonstrated to have a three-layer structure, with the inner and middle layers having a common, logarithmic overlap. The inner layer is exponentially thin compared to the middle layer, but is not affected by the pressure gradient. Rotational forces are considered to be located in the middle layer. Wake and wall functions are formulated to generate the velocity profiles in each region, together with the streamwise and crossflow components. Comparisons with experimental data demonstrate the accuracy of the three dimensional mmodel...