Development of a complete model of turbulence revisited

A comprehensive and critical review of closure approximations for two equation turbulence models has been made. Particular attention has focused upon the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this report demonstrates: (1) conventional k-e and k-omega sq formulations generally are inaccurate for boundary layers in adverse pressure gradient; (2) using so-called wall functions tends to mask such models' shortcomings; and (3) there exists a more suitable choice of dependent variables which is far more accurate for adverse pressure gradient.