Gravity waves with effect of surface tension and fluid viscosity

The potential flow in a viscous fluid due to a point impulsive source is considered within the framework of linear Stokes equations. The combined effect of fluid viscosity and surface tension on the potential function below and on the water surface is studied. Dependent on the wavenumbers associated with the level of the effect due to surface tension, the oscillations can be grouped as gravity-dominant waves and capillary-dominant waves. It is shown that the wave form of gravity-dominant oscillations is largely modified by the surface tension while the wave amplitude of capillary-dominant oscillations is mostly reduced by the fluid viscosity.