Computation of free-surface flows under the influence of pressure distribution

Steady two-dimensional flows due to an applied pressure distribution in water of finite depth are considered. Gravity is included in the dynamic boundary condition. The problem is solved numerically by using the boundary integral equation technique. It is shown that, for both supercritical and subcritical flows, solutions are characterized by three parameters: (i) the Froude number, (ii) the magnitude of applied pressure distribution and (iii) the span length of applied pressure distribution. For supercritical flows, there exist up to two solutions corresponding to the same value of Froude number for positive pressures and a unique solution for negative pressures. For subcritical flows, there are solutions with wave behind the applied pressure distribution. As the Froude number decreases, these waves diminish when the Froude numbers approach the critical values. The surface tension effect is also investigated in the case of subcritical symmetric flows. It is found that for some values of the Bound number and positive pressures, there exist limiting cofigurations with trapped bubble as the Froude number approaches a critical value (near zero). On the other hand, the free surface profile tends to develop a large number of inflexion points as the Froude numbers approach 1