Capillary-gravity waves: The effect of viscosity on the wave resistance

The effect of viscosity on the wave resistance experienced by a two-dimensi onal perturbation moving at uniform velocity over the free surface of a flu id is investigated. The analysis is based on Rayleigh's linearized theory o f capillary-gravity waves. It is shown in particular that the wave resistan ce remains bounded as the velocity of the perturbation approaches the minim um phase speed c(min) = (4g gamma/rho)(1/4) (rho is the liquid density, gam ma is the liquid-air surface tension, and g the acceleration due to gravity ), unlike what is predicted by the inviscid theory.