Asymptotic analysis of the turbulent boundary layer of an incompressible fluid

In the present paper, the turbulent incompressible boundary layer is analyzed by the method of internal and external asymptotic expansions. It is shown that the entire flow area in the boundary layer can be broken down into three characteristic zones: a zone governed by the law of velocity defect, an intermediate zone, and a viscous zone. The equations derived cannot be closed in any of the zones. The thickness of the zone is expressed in terms of the Reynolds number and the characteristic value of the dynamic velocity at the wall. It is shown that Karman's friction law does not follow from the conditions of asymptotic joining of solutions.