The problem of predicting the behavior of the incompressible turbulent boundary layer in an adverse pressure gradient is re-examined. An outline of the problem is given along with a brief summary of the work that has already been done, including both experimental investigation are presented for a separating turbulent boundary layer with various pressure distributions. An approximate theory is developed in which the momentum integral equation is satisfied for each half of the boundary layer. The velocity profiles used in the analysis consist of the well known wall and wake regions, resulting in a two-parameter family with the Reynolds number as one parameter. It is assumed, with some experimental justification, that the eddy viscosity can be reasonably approximated from zero pressure gradient experimets. The numerical calculations, using the Runge-Kutta procedure, show good agreement with the experiments. The reliability that can be expected of such approximate methods is discussed. (Author).

Experimental data for skin friction of turbulent boundary layers under adverse pressure gradient are presented from several sources. Data obtained by momentum balance are shown to follow a trend opposite to that of data obtained by a hot-wire and heat-transfer methods. A new integral energy parameter and a new momentum thickness are introduced. The momentum equation and total-head measuring techniques are discussed in relation to skin-friction computation.

Shear stress, eddy viscosity, and mixing length distributions corresponding to five two-dimensional, incompressible equilibrium turbulent boundary layers were calculated by substituting measured velocity profile data into the governing equations. The five flows cover the range from moderate adverse pressure gradient to strong favorable pressure gradient. (Modified author abstract).

This report describes the results of analytical, numerical, and experimental investigations of incompressible and compressible boundary layers. The subjects considered are (1) Laminar and/or turbulent numerical boundary-layer calculations in which the Reynolds stress is related to the turbulent kinetic energy; (2) an analytical investigation of turbulence near a wall which is not founded on classical mixing-length theory; (3) analytical solutions for relating velocity and temperature throughout turbulent boundary layers for nonunity Prandtl numbers; (4) a description of the data reduction of pitot pressure measurements utilizing these analytical results, and (5) the application of the numerical and analytical results to the analysis of turbulent boundary-layer measurements made in the Propulsion Wind Tunnel Facility (PWT).