Free surface flow under gravity and surface tension due to an applied pressure distribution: I Bond number greater than one-third

Abstract

We consider steady free surface two-dimensional flow due to a localized applied pressure distribution under the effects of both gravity and surface tension in water of constant depth, and in the presence of a uniform stream. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The behavior of the forced nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, τ > 1/3, and the magnitude and sign of the pressure forcing parameter ɛ. The fully nonlinear wave problem is solved numerically by using a boundary integral method. For small amplitude waves and F 1/3, there exists both elevation and depression waves. In some cases, a limiting configuration in the form of a trapped bubble occurs in the depression wave solutions.