Mellor, G. L., 1967: Incompressible, turbulent boundary layers with arbitrary pressure gradients and divergent or convergent cross flows. American Institute of Aeronautics and Astronautics (AIAA) Journal, 5 (9), 1570-1579.

Abstract: An effective viscosity hypothesis that has previously led to rather detailed predictions of equilibrium turbulent boundary layers is now applied to boundary layers with arbitrary mainstream pressure variations and with divergent or convergent cross flows. The empirical content of the hypothesis involving three empirical constants (one of which is the von Karman constant) is solely derived from constant pressure profile data. The present work is similar to the previous work in that the mean differential equations of motion are integrated numerically. This time, however, one must deal with partial differential equations instead of the ordinary differential equations applicable to equilibrium flows. An important result is that prediction of the skin-friction coefficient and separation is very good. For the data considered, it is apparent that the effective viscosity hypothesis is not restricted to equilibrium flows; a corollary is that the effective viscosity can be related to the local mean velocity profile to some reasonable but undetermined degree of approximation. A further result is that for a particular three-dimensional, divergent flow experiment the measured cross- flow profiles agree with those calculated using a scalar-effective viscosity.