Fully developed free surface flows-Liquid layer flow over a convex corner

The paper discusses the steady flow of a liquid layer over a convex corner at high Reynolds number (R). A double decked structure for the flow is proposed with the displaced free surface equal to the locla boundlary layer displacement (-A), and the pressure P being determined by the law P = -sA - A″. Here s is inversely proportional to the angle of inclination of the initial plane. Linearized solutions are obtained for small angles and numerical calculations are carried out for much larger angles, with the plane at various inclinations. The unusual breakdown of the linear theory downstream is also discussed. The computer results and the asymptotic description far downstream show that the flow does not return to its undisturbed state; instead the layer continues to get thinner with the fluid moving much faster. It is suggested that this feature may be resolved on a longer lengthscale. The analysis presented applies equally to a more general fully developed profile at large Froude numbers and extra features such as surface tension can be incorporated into the basic formulation without formal difficulty. © 1987.