Axisymmetric waves of small amplitude on the interface between two viscous fluids

Axisymmetric wave of small amplitude on the interface between two viscous fluids is studied. The amplitude of wave is solved as a function of time. Two single-fluid cases in which one of the fluids has negligible dynamic effect are considered. The small and large time approximations are obtained and compared with the exact solution. It is found that the small time approximation is valid for small wave numbers or small viscosity; generally the large time approximation is accurate only at large times. The characteristic of vorticity is affected by wave number and viscosity significantly.