A critical examination of the use of a two-dimensional turbulent profile family to represent three-dimensional boundary layers

Abstract

The streamwise velocity profile is established as the most suitable basic profile for the calculation of three-dimensional turbulent boundary layers. Measured streamwise profiles are compared with Thompson's two-dimensional profile family and it is shown that the discrepancies produced by the variation of flow direction within the boundary layer, the pressure gradient normal to the external flow and the convergence or divergence of the flow are generally small. The result of the streamwise pressure gradient (which is as much a two-dimensional as a three-dimensional effect) can, however, be very appreciable. The four effects listed above are expressed as non-dimensional parameters and limits are suggested within which the streamwise profile is likely to be moderately well represented by Thompson (or similar) two-dimensional profiles. Some consideration is given to the associated problem of estimating the coefficient of skin friction in three-dimensional boundary layers and some alternative methods are compared.