Gravity-Capillary Lumps Generated by a Moving Pressure Source

The nonlinear wave pattern generated by a localized pressure source moving over a liquid free surface at speeds below the minimum phase speed (c_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_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_c≈0.9c_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_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.