An approximate solution of the turbulent boundary layer equations in incompressible and compressible flow

If over the ‘outer’ region/ of the boundary layer, where the mean velocity varies but little from its value outside the shear layer, a virtual eddy viscosity is defined, which is constant over the outer region but varies in the direction of the mainstream, a solution of the turbulent boundary layer equations can be found which satisfies the appropriate boundary conditions. The solution leads to a compatibility condition for the virtual eddy viscosity in terms of the wall shear stress, the boundary layer momentum thickness and the mainstream velocity, at least for the case of a constant external velocity. [...cont.]