Equilibrium and non-equilibrium turbulent boundary layers

This article presents a review of historical and recent developments in the understanding of equilibrium and non-equilibrium turbulent boundary layers at incompressible high-Reynolds number conditions. The most fundamental equations and concepts are first introduced to provide a basis and context for the material reviewed. The review focusses on findings concerning the mean flow and turbulence stress fields, as well as on major elements of the instantaneous structure. Zero pressure gradient smooth wall and rough wall boundary layers are described, forming the basis of following material on equilibrium boundary layers formed in favorable and adverse pressure gradients. Non-equilibrium two dimensional flows formed in pressure gradient, with and without roughness, and as a result of step changes in roughness are covered. A detailed discussion of the physics and mathematics unique to the development of boundary layers in skewed, three-dimensional flows over smooth walls concludes the review.