An incompressible three-dimensional turbulent boundary layer on the floor of a recurving rectangular channel

A brief review of three-dimensional turbulent boundary layer mean velocity profile models was presented, with emphasis on the applicability of these to predict cross flow profiles when skewing existed in any single profile.

A recurving or s-shaped rectangular channel was used to experimentally investigate the possible existence of such a turbulent boundary layer flow. The time average velocity profiles along the centerline of this channel were obtained with a hot film anemometer.

The resultant profiles indicated that a turbulent boundary layer can exist with cross flow in two lateral directions simultaneously in the same profile and this phenomenon can occur over a relatively long flow distance. Several attempts were made to fit the models of Eichelbrenner and Shanebrook to the measured cross flow profiles, but with only limited success. A test of the three-dimensional wall-wake formulation proposed by Coles was made for each profile. A shear velocity was inferred by a modification of the two-dimensional Ludwieg and Tillman skin friction equation, and by a modified form of the two-dimensional Clauser skin friction chart. A linear semi-logarithmic region was judged distinguishable for profiles with skewing in one lateral direction and with the limiting wall streamline angle less than approximately 30 degrees. Additionally in some instances a linear semi-logarithmic region was judged to exist when when simultaneous lateral skewing occurred in two directions.

Generally, the constructed wake profiles did not resemble the universal form tentatively proposed by Coles, but rather resembled the characteristic preasymptotic form as discussed by Pierce.