THE FREE-SURFACE FLUID-FLOW OVER A STEP OF AN ARBITRARY SHAPE IN A CHANNEL

A boundary integral technique has been developed for the two-dimension al, free surface fluid flow in an arbitrary shaped channel. For steady , ideal, irrotational fluid flow a system of boundary integral equatio ns are derived which are based on the Riemann-Hilbert technique for mi xed boundary value problems of an analytical function. The boundary in tegral equations are solved for the fluid speed on both the solid boun dary and the free surface, the shape of the free surface and for the c ritical Froude number for which waves first occur. (C) 1997 Elsevier S cience Ltd.