THE AXISYMMETRIC TURBULENT BOUNDARY LAYER ON AN EXTREMELY LONG CYLINDER

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.