Thick axisymmetric turbulent boundary layer on a circular cylinder

Two similarity laws for a thick, axisymmetric, turbulent boundary layer on a long circular cylinder are presented. In the law-of-the-wall region, the validity of the assumption of a constant-stress moment is analyzed and a new logarithmic mixing-length model, which takes into account the transverse-curvature effect on turbulence, is proposed. Using this mixing-length model, a law of the wall is derived which is given in terms of the exponential integral in the logarithmic portion. When the boundary layer is very thick relative to the radius of the cylinder, the flow in the outer region of the boundary layer is similar to an axisymmetric wake. With this analogy, a velocity-defect law is derived in terms of confluent hypergeometric functions known as Kummer functions. Both similarity laws are compared with the available data.