Serre-Green-Naghdi Dynamics under the Action of the Jeffreys’ Wind-Wave Interaction

We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in context of nonlinear dynamics surface water waves under wind forcing, finite depth. The anti-dissipation occurs du to continuos transfer energy wave. find solitary wave solution system, with an increasing amplitude action. This leads blow-up time for infinitely large asymptotic space. dispersive, anti-dissipative and fully phenomenon is equivalent linear instability at infinite time. theoretical calculated based on real experimental data. Naturally, breaking takes place before However, amplitude’s growth resulting could be observed. Our results show that, particular type wind-wave tank data used this paper, h=0.14m, rate order 0.1 which experimentally, measurability limit. But we think that by gradually speed U10, up 10 m/s, it possible have confirmation present theory existing facilities.