Effect of film elasticity on the drift velocity of capillary–gravity waves

The effect of an insoluble, elastic surface film on the drift velocity of capillary–gravity waves is studied theoretically on the basis of a Lagrangian description of motion. There is no forcing from the atmosphere, and the wave amplitude is taken to attenuate in time. Defining a nondimensional parameter α, which combines film elasticity, fluid viscosity, and wave frequency, maximum damping of the linear waves occurs when α=1 (the Marangoni effect). In this case the frequency of capillary–gravity waves nearly coincides with that of elastic film waves. The nonlinear drift velocity is obtained for general values of α. In particular, it is found that the absolute maximum of the transient drift current is located below the surface when α≳2/3. At the surface, maximum drift velocity (in time domain) occurs for values of α that are somewhat less than one.