Gravity-Capillary Lumps Generated by a Moving Pressure Source

Abstract

The nonlinear wave pattern generated by a localized pressure source moving over a liquid free surface at speeds below the minimum phase speed (c [subscript min]) of linear gravity-capillary waves is investigated experimentally and theoretically. At these speeds, freely propagating fully localized solitary waves, or ‘‘lumps,’’ are known theoretically to be possible. For pressure-source speeds far below c[subscript min], the surface response is a local depression similar to the case with no forward speed. As the speed is increased, a critical value is reached c[subscript c]≈0.9c[subscript min] where there is an abrupt transition to a wavelike state that features a steady disturbance similar to a steep lump behind the pressure forcing. As the speed approaches c[subscript min], a second transition is found; the new state is unsteady and is characterized by continuous shedding of lumps from the tips of a V-shaped pattern.