Free-surface flows over submerged obstacles

Abstract

We consider free-surface flows over submerged obstacles under the effects of gravity and surface tension. The fluid is treated as inviscid and incompressible. The flow is assumed to be steady, two-dimensional, and irrotational. The flow is characterized by the following parameters: Froude number F, Bond number Bo, distance between the obstacles x[subscript d], and height of the obstacles hob. Fully nonlinear problem is solved numerically by using the boundary integral equation technique. After the discretization, we obtain a system of nonlinear algebraic equations which can be solved by the Newton’s method. In addition, the weakly nonlinear problem of steady and time-dependent flows are investigated and compared with the fully nonlinear results. In this thesis, special case of flows over a single obstacle is summarized in the solution diagram of (F, hob)-plane for bump(hob > 0) and dip (hob < 0). New family of solutions of free-surface flows over two obstacles are proposed.