Effects of Surface Tension over a Flow Past a Flat Plate

Abstract

We consider a free surface flow past a flat plate. We consider relations between the results of Anderson and Vanden-Broeck (1996) and those of Osborne and Stump (2000), and present new solutions. There is need to know the number of parameters needed to fix solutions uniquely. We show here that there is a three parameter family of solutions when the fluid is of finite depth. These solutions are characterised by a train of waves in the downstream region and by a discontinuity in slope at the separation point. The family includes a two parameter sub-family for which the free surface leaves the plate tangentially. It is shown that this sub-family reduces to the linear solutions of Osborne and Stump (2000) when the depth of submergence of the plate is small. Also, the three parameter family reduces to the one parameter family of Anderson and Vanden-Broeck (1996) as the depth of the water tends to infinity. Finally, fully nonlinear solutions with large capillary waves are presented.