Free-surface flows past a surface-piercing object of finite length

Abstract

Steady two-dimensional flows past a parabolic obstacle lying on the free surface in water of finite depth are considered. The fluid is treated as inviscid and incompressible and the flow is assumed to be irrotational. Gravity is included in the free-surface condition. The problem is solved numerically by using boundary integral equation techniques. It is shown that there are solutions for which the flow is supercritical both upstream and downstream and others for which the flow is subcritical both upstream and downstream. These flows have continuous tangents at both ends of the obstacle at which separation occurs. For supercritical flows, there are up to three solutions corresponding to the same value of the Froude number when the obstacle is concave and up to two solutions when the obstacle is convex. For subcritical flows, there are solutions with waves behind the obstacle. As the Froude number decreases, these waves become steeper and the numerical calculations suggest that they, ultimately, reach limiting configurations with a sharp crest forming a 120° angle.