The properties of equilibrium boundary layers

Abstract

The recent work on equilibrium (i.e. self-preserving) turbulent boundary layers in adverse pressure gradients is compared with theoretical predictions based on current generalizations about the turbulent shear flow. Using only assumptions of similarity, it is possible to show that an equilibrium layer can exist only if the free stream velocity varies as a power of distance downstream with an exponent greater than − and if the velocity defect from the free stream is small. Assuming further that the effective eddy viscosity is independent of distance from the wall over the outer part of the layer, most of the properties of equilibrium layers may be computed from the known behaviour of layers in zero pressure gradient. The predicted values of skin friction and the predicted shape and magnitude of the mean velocity distribution are in fair agreement with the observations of Clauser. Finally, the modifications that are necessary if the velocity defect is not small are discussed briefly.