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

Hysteresis phenomena in forced gravity-capillary waves on deep water where the minimum phase speed cmin D 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. © 2019 Cambridge University Press.