Criterion for the detachment of laminar and turbulent boundary layers

A criterion is proposed for the detachment of incompressible, steady, two-dimensional boundary layers under the influence of adverse pressure gradients on smooth, faired surfaces, in the absence of heat or mass transfer. It is proposed that detachment will occur if a suitably defined dimensionless parameter measuring the ratio of the boundary-layer momentum defect to the freestream momentum reaches a maximum value. The approach requires knowledge of the relations between integral thicknesses during separation, but no empirically determined critical value is required for any boundary-layer shape factor. Consensus values of such parameters follow accurately from the proposed procedure. The criterion is exact in the context of the Karman-Pohlhausen theory and precisely satisfied by numerically evaluated solutions of the Falkner-Skan equation. The criterion is consistent with Simpson's experimental data and compares well with several established semi-empirical methods for predicting the intermittent transitory detachment of turbulent boundary layers.