A new approach to the study of fundamentally and practically interesting class of high speed wall bounded turbulent "shear" flows will be presented and briefly discussed. This approach, based on a combination of incomplete similarity and vanishing viscosity asymptotics, was proposed in recent years by our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and the present author). It revealed in particular that the classical "logarithms" law, generally considered to be one of the cornerstones of the theory of turbulence and widely used in engineering practice and education, is not quite correct: the seemingly plausible basic assumption that the influence of viscosity does not penetrate to the core of the flow but remains concentrated in a narrow vicinity of the wall, had to be reconsidered. A new "scaling" (power) law for the mean velocity profile, taking into account the overall influence of viscosity, was obtained. A detailed comparison with experimental data for turbulent flows in pipes and boundary layers demonstrated an instructive agreement. The results obtained suggest new possibilities for further studies of a wide class of fundamentally and practically interesting flow such as turbulent jets, mixing layers, etc. The new approach also reveals certain general properties of developed turbulent flows.