Ermakov S.A., Khazanov G.E. «Double-resonance damping of gravity-capillary waves on water covered with a viaco-elastic film of finite thickness» Волны и вихри в сложных средах: 13 международная конференция – школа молодых ученых; 30 ноября–02 декабря 2022 г., Москва: Сборник материалов школы, с. 15-16 (2022)

Analysis of gravity-capillary wave (GCW) on the water surface covered with films of organic surfactants or mineral oils is very important in the context of the problem of ocean pollutions and their remote sensing. A hydrodynamic theory of GCW developed in a number of papers shows that surfactant films can strongly enhance the GCW damping coefficient (DC). One of the most interesting features is that DC reaches a maximum at certain finite values of the film elasticity, not at infinite elasticity. Apart from GCW another type of wave motion can exist in a viscous fluid with an elastic surface. This motion corresponds to quasi horizontal oscillations in a viscous boundary layer below a film, so-called Marangoni waves (MW). An intriguing feature has been revealed that the maximum of the GCW DC corresponded to MW which frequencies and wavelengths were roughly close to those of GCW, i.e. when the two wave modes were is “resonance”. A hypothesis was proposed and became very common in the literature that the GCW damping maximum is due to the resonance absorption of GCW energy by MW. An alternative explanation of GCW resonance–like damping due to an infinitely thin film was developed by Dysthe and Rabin (1986) and later by Ermakov (2003). It has been shown that GCW contain a rotational (r-) component which can be described formally as MW ”excited” by the potential (p-) component of GCW, and this excitation is the most effective and, correspondingly, DC has a maximum when the frequencies and wave numbers of GCW and MW are close to each other. In this work the mentioned approach is used for analysis of GCW damping due to films of finite thickness with elastic boundaries, e.g. for oil/oil product films