Effect of Viscosity on Free-Surface Waves in Oseen Flows

Based on the complex dispersion relation for the two-dimensional free-surface waves generated by a moving body in the steady Oseen flows, the effect of viscosity on wavelength and wave amplitude was investigated by means of an asymptotic method and a numerical analysis. A comparison between the asymptotic and numerical analysis for the viscous decay factor demonstrates the validity of the perturbation expansions for the wave profile. The numerical result shows that the wavelength of viscous wave is slightly elongated in comparison with that of inviscid wave.