A Physical Approach to Turbulent-Boundary-Layer Problems

A new approach to the problem of incompressible, turbulent boundary layers is presented. From physical considerations involving the diffusion of turbulent stresses, the boundary layer is divided into three regions distinguished by the relative proximity of the wall. Within a distance of approximately 10% of the boundary-layer thickness from the wall, the local wall conditions have an important effect whereas the outer 75% is governed entirely by the spatial history of the boundary layer. The inner region includes the laminar sublayer, the buffer zone, and that part of the turbulent region characterized by the logarithmic velocity profile. The outer region of the turbulent boundary layer is similar to that of a wake or jet, being characterized by a sharp but irregular boundary between turbulent and nonturbulent regions. Here the velocity profile may usually be approximated by a 3/2-power deficiency relationship. The region between the inner and outer parts is a blending region more complicated than either of the other two and not easily analyzed. This new physical analysis, combined with empirical correlations, leads to a new method for computing two-dimensional turbulent boundary layers. The method usually involves only algebraic equations and is more versatile than any previously published method.