Hysteresis phenomena in gravity-capillary waves on deep water generated by a moving two-dimensional/three-dimensional air-blowing/air-suction forcing

Abstract

Hysteresis phenomena in forced gravity–capillary waves on deep water where the minimum phase speed cmin=23 cm s−1 are experimentally investigated. Four kinds of forcings are considered: two-dimensional/three-dimensional air-blowing/air-suction forcings. For a still-water initial condition, as the forcing speed increases from zero towards a certain target speed ( U ), there exists a certain critical speed ( Ucrit ) at which the transition from linear to nonlinear states occurs. When U<Ucrit , steady linear localized waves are observed (state I). When Ucrit<U<cmin , steady nonlinear localized waves, including steep gravity–capillary solitary waves, are observed (state II). When U≈cmin , periodic shedding phenomena of nonlinear localized depressions are observed (state III). When U>cmin , steady linear non-local waves are observed (state IV). Next, with these state-II, III and IV waves as new initial conditions, as the forcing speed is decreased towards a certain target speed ( Ufinal ), a certain critical speed ( Ucrit,2 ) is identified at which the transition from nonlinear to linear states occurs. When Ucrit,2<Ufinal<Ucrit , relatively steeper steady nonlinear localized waves, including steeper gravity–capillary solitary waves, are observed. When Ufinal<Ucrit,2 , linear state-I waves are observed. These are hysteresis phenomena, which show jump transitions from linear to nonlinear states and from nonlinear to linear states at two different critical speeds. For air-blowing cases, experimental results are compared with simulation results based on a theoretical model equation. They agree with each other very well except that the experimentally identified critical speed ( Ucrit,2 ) is different from the theoretically predicted one.