The continuously critical turbulent boundary layer

Abstract

The problem of the turbulent boundary layer in two-dimensional, incompressible flow, which is continuously critical, i.e. on the point of separating, over part of its length is solved by combination of the Buri separation criterion with the boundary-layer momentum equation. In the latter an attempt is made to allow for transverse pressure variation and Reynolds stresses by over-estimating the contribution of skin friction. The Buri constant is taken to have a value of Γ =−0·04. Whereas Stratford and Townsend assumed that an initially noncritical boundary layer could be transformed instantaneously into a critical state by the application of an infinite pressure gradient at a point, in the present approach it is considered necessary to induce a critical state over a finite length, this state then being maintained downstream. These solutions are thus not comparable near the starting-point of the flow, but fair agreement is suggested at large distances downstream, with Stratford and Townsend's theoretical solutions and with Stratford's experimental data.Comparison is also made with an ideal pressure distribution suggested by Stuart and the basis of optimization is discussed. It is suggested that the optimum flow might be similar in form to the continuously critical flow. The thesis that a continuously critical boundary-layer flow is ideal for large extents of the suction surface of an aerofoil is denied.The paper concludes that the Buri criterion is valid but that in this case the Buri constant has a value of -0·04 rather than the accepted value of -0·06. Previous work by the author in connexion with cascade aerofoils is justified. The analysis predicts theoretical minimum diffusion lengths for given pressure rises provided that the initial boundary layer has achieved a critical condition.