EVOLUTION CALCULATIONS FOR TURBULENT BOUNDARY LAYERS APPROACHING EQUILIBRIUM SINK FLOW I MARUSIC A E PERRY M B JONES and M S CHONG Department of Mechanical and Manufacturing Engineering

th Australasian Fluid Mechanics Conference Monash University Melbourne Australia December The evolution of a turbulent boundary layer ap proaching a smooth wall equilibrium sink ow is con sidered The closure problem is described for the gen eral arbitrary pressure gradient ow where the only assumptions made are the use of the classical similar ity laws such as Prandtl s law of the wall and Coles law of the wake together with the mean continuity and mean momentum di erential and integral equa tions The important parameters are identi ed and the problem reduces to one semi empirical input with the assumption that the Reynolds shear stress can be described by a two parameter family Good agree ment is shown with experimental data INTRODUCTION Perry Marusic Li initially developed a mathematical framework for computing the evolution of turbulent boundary layers using the classical simi larity laws such as Prandtl s law of the wall and Coles law of the wake together with the momentum integral and di erential equations It was found that these equations show that there are parameters which control the streamwise evolution of the layer and the Reynolds shear stress distribution and these are S and S U U where U is the local freestream velocity and U is the friction velocity is Coles wake factor dp dx is the Clauser pressure gradient parameter where is the displacement thickness p is the freestream static pressure is the wall shear stress and x is stream wise distance and S cd dx where c is the boundary layer thickness The total shear stress is expressed as