The compressible axisymmetric laminar boundary layer is considered for very large values of the transverse curvature parameter (roughly proportional to the ratio of the Mangler value of the boundary layer displacement thickness to the local cross-sectional radius of the body). Asymptotic expansions are constructed using the method of inner-outer expansions and verified by comparison with exact numerical similarity solutions. Both finite and hypersonic Mach number inviscid flow conditions are considered. The principal results are asymptotic formulas for skin friction, heat transfer, and boundary layer displacement thickness. Existing expansions, obtained by Wei, are found to be incorrect. The viscous pressure interaction near the vertex of a pointed axisymmetric body is treated within the framework of boundary layer theory and a tangent-cone approximation. (Author).

The compressible axisymmetric laminar boundary layer is considered for very large values of the transverse curvature parameter (roughly proportional to the ratio of the Mangler value of the boundary layer displacement thickness to the local cross-sectional radius of the body). Asymptotic expansions are constructed using the method of inner-outer expansions and verified by comparison with exact numerical similarity solutions. Both finite and hypersonic Mach number inviscid flow conditions are considered. The principal results are asymptotic formulas for skin friction, heat transfer, and boundary layer displacement thickness. Existing expansions, obtained by Wei, are found to be incorrect. The viscous pressure interaction near the vertex of a pointed axisymmetric body is treated within the framework of boundary layer theory and a tangent-cone approximation. (Author).

An approximate momentum integral solution for the compressible axisymmetrix laminar boundary layer when transverse curvature effects are important is presented. Both finite and infinite inviscid Mach numbers are considered. Detailed comparisons with exact asymptotic solutions are given. The method is found, in many instances, to agree to leading order with the exact solutions as the transverse curvature becomes very large--a property that none of the existing approximate solutions for compressible flow possess. Some example calculations for a cone in supersonic and hypersonic flow are presented. Also, the method is applied to the hypersonic self-induced pressure problem for a cone. (Author).

Use is made of self similarity approach and integral momentum technique to obtain solutions of Van Dyke's second-order boundary-layer equations for laminar incompressible flow. Accurate numerical solutions of the most general self similar equations are tabulated for the four second-order contributions due to vorticity interaction, displacement speed, longitudinal curvature, and transverse curvature. A limited number of closed form solutions are obtained which appear to have special significance at the point of first-order boundary-layer separation. In particular it is found that the displacement speed problem can proceed up to separation for only two values of the second-order pressure gradient. All other cases display an infinite discontinuity at this point. Numerical solutions of a large number of cases for the longitudinal and transverse curvature effects well support an identical conclusion. The integral momentum technique applied (a straight forward extension of the Karmen-Pohlhausen solutions) is found to be oversensitive to approximations and in the final analysis is rejected in favor of locally similar solutions. (Author).

An analysis is presented which predicts the properties of an arbitrarily thick turbulent boundary layer in axial flow past a long cylinder. The study makes use of a modified form of the turbulent law-of-the-wall, which properly accounts for transverse curvature effects. Using this law, the theory which follows is then an exact solution to the axisymmetric equations of continuity and momentum in incompressible flow. Numerical results are given to show the effect of curvature on the various boundary layer characteristics. Skin friction and drag coefficients can be increased greatly with increasing curvature while boundary layer thickness is decreased. When defined in their axisymmetric form, the displacement and momentum thickness are both decreased by curvature. The velocity profile is flattened greatly and the shape factor approaches unity at large curvature. The failure of earlier power-law theories to make accurate predictions is shown to be due to their inadequate handling of the strong profile shape changes. (Author).