Damping of gravity–capillary waves on water surface covered with a visco-elastic film of finite thickness

Results of laboratory studies of the damping of gravity–capillary waves on a water surface covered with a film of petroleum product (diesel fuel) in a wide range of change in a film thickness are presented. A nonmonotonic dependence (with a local maximum) of a damping coefficient on film thickness is discovered. Numerical calculations of the dispersion equation for gravity–capillary waves in the presence of a viscoelastic film of arbitrary thickness, which confirmed the existence of the maximum of the damping coefficient as a function of film thickness, are performed. Based on a comparison of the calculation results and the data of laboratory measurements of wave characteristics, the values of parameters in the diesel fuel films are estimated in a wide range of a change in their thickness.