Coordinate transformation for laminar and turbulent boundary layers

A composite transformation based entirely on fluid dynamics concepts is given for the simultaneous capture of the two turbulent length scales, i.e., the boundary-layer thickness and the wall-layer thickness. The proposed approach involves the following principal steps: (1) a transformation is employed for the capture of the boundary-layer thickness using a turbulent generalization of the Levy-Lees variables; (2) a coordinate is established for the capture of a turbulent wall-layer region; and (3) a composite coordinate is established using matching concepts. The utility of the approach is demonstrated through its application in a finite-difference solution of the boundary-layer equations in which the scheme is shown to be uniformly applicable to laminar, transitional, and turbulent flow.