Influence of surface tension on free-surface flow over a polygonal and curved obstruction

Abstract

In a previous study by the author (1993), the two-dimensional steady flow of a fluid over a polygonal and curved obstruction on the bottom of a stream is discussed, and a linearized solution for the free-surface profile is obtained. This study is generalized to include the effects of surface tension. A linearized theory based upon small elevations or depressions in the bottom is presented, in which the existence of three different branches of solutions is predicted, depending on the Froude number and the surface tension. The results are plotted for two special shapes of the bottom, in the different domains of solution.