Gravity-capillary water waves generated by multiple pressure distributions

Steady two-dimensional free-surface flows subjected to multiple localised pressure distributions are considered. The fluid is bounded below by a rigid bottom, and above by a free-surface, and is assumed to be inviscid and incompressible. The flow is assumed irrotational, and the effects of both gravity and surface tension are taken into account. Forced solitary wave solutions are found numerically, using boundary integral equation techniques, based on Cauchy integral formula. The integrodifferential equations are solved iteratively by Newton's method. The behaviour of the forced waves is determined by the Froude number, the Bond number, and the coefficients of the pressure forcings. Multiple families of solutions are found to exist for particular values of the Froude number; perturbations from a uniform stream, and perturbations from pure solitary waves. Elevation waves are only obtained in the case of a negatively forced pressure distribution.