A new approach to the problem of damping of gravity-capillary waves (GCW) on water covered with a layer of viscous liquid (a film) of finite thickness with two elastic boundaries is developed. It is shown that the rotational component of GCW can be described formally as a "forced" longitudinal, or Marangoni wave (MW) and the potential component of GCW plays a role of the "external force". The resonance -like excitation of the "forced" MW is demonstrated when the GCW and MW frequencies and wave numbers are approximately close to each other. For a film which is thinner than the viscous boundary layers in film a single "forced" MW exists being located within the boundary layer beneath the water surface. For a thick film the "forced" MW is characterized by the existence of two spatially separated MW modes: one is localized in the boundary layer below the upper, air-film interface and another within the boundary layers in the vicinity of the water-film interface. Then at different elasticities of the interfaces a double peak dependence of the GCW damping coefficient on wave number can occur due to the resonance with the two "forced" MW modes. The dependence of the damping coefficient on film thickness is characterized by a strong maximum appearing when the film and boundary layer thickness values are comparable to each other. The developed theory is consistent with existing numerical studies and experiment.
The paper considers environmental problems of hydrocarbon fuel usage. The assessment of the area necessary for cultivation of algae biomass and its further use as solid fuel at thermal power plant has been carried out. Expediency of production of microalgae biomass in the process of photosynthesisas raw material for biofuel production is revealed.
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