Separation criterion for turbulent boundary layers via similarity analysis

By using the RANS boundary layer equations, it will be shown that the outer part of an adverse pressure gradient turbulent boundary layer tends to remain in equilibrium similarity, even near and past separation. Such boundary layers are characterized by a single and constant pressure gradient parameter, Λ, and its value appears to be the same for all adverse pressure gradient flows, including those with eventual separation. Also it appears from the experimental data that the pressure gradient parameter, Λ _θ, is also approximately constant and given by Λ _θ =0.21 ±0.0J. Using this and the integral momentum boundary layer equation, it is possible to show that the shape factor at separation also has to within the experimental uncertainty a single value: H _sep≅2.76±0.23. Furthermore, the conditions for equilibrium similarity and the value of H _sep are shown to be in reasonable agreement with a variety of experimental estimates, as well as the predictions from some other investigators.