Free surface flow under a gate with gravity and surface tension effect

Abstract

In this work, we consider a two dimensional free-surface flow of an inviscid and incompressible fluid under an inclined gate of an angle gamma. The flow is assumed to be steady and irrotational. The effect of surface tension and gravity are taken into account on both upstream and downstream free surfaces. The flow is characterized by the following parameters, Froude number Fr and the inverse Weber number delta. Fully nonlinear problem is solved numerically by using boundary integral equation technique. After discretization, we obtain a system of nonlinear algebraic equations which can be solved by Newton's method. When the upstream free surface separates at a stagnation point, nonlinear effect on the upstream waves is apparent so that the waves tend to develop narrow crests and broad troughs. Numerical results for inclined gate are presented and discussed for various values of the inverse Weber number and the Froude number.

Keywords

• integro-differential equations
• surface tension
• inclined gate
• froude number