Numerical calculation of steady gravity-capillary waves forced by a surface pressure distribution

Steady free-surface flow due to a pressure distribution under both gravity and capillary effects in water of finite depth is considered. The fluid is assumed to be inviscid and incompressible and the flow is irrotational. The problem is formulated as an integro-differential equation. Numerical results are found to depend on three parameters: Froude number, F , Bond number, τ∗, and the magnitude and sign of the pressure forcing, . In this study, we restrict attention to the case of symmetric subcritical flow (F < 1). It is found that, for given values of τ∗ and , there exist both elevation and depression waves. In some cases, the limiting configuration in the form of a trapped bubble occurs in the depression wave solutions.