A Review of Near-Wall Similarity Models in Three-Dimensional Turbulent Boundary Layers

Abstract

Eleven near-wall similarity models for three-dimensional turbulent boundary layers which have been identified in the literature are reviewed. Each model summary includes a brief review of its derivation, discusses limitations in the derivation, estimates the applicable y+ range, and compares differences among the models. This review of three-dimensional similarity models was developed as part of a larger study which tests the validity of ten of these different models by comparison with experimental data which includes the direct and simultaneous measurement of the local wall shear stress direction and magnitude in a three-dimensional turbulent flow. A direct force measurement of local wall shear stress is necessary to test the local wall shear-shear velocity relationship, τ0 = ρq*2, generally assumed in three-dimensional flows. This review is necessary to acquaint the reader with the similarities and differences among the models tested in companion papers since differences among some of the models are significant, particularly in the coordinate systems of the vector models.