Viscous Damping of Stationary Wave Formed Near an Obstacle in a Channel

Abstract

The purpose of this study is to investigate surface wave damping due to viscosity. The stationary wave formed near an obstacle in a horizontal channel is chosen as the subject of this analysis because gravitational and surface tension waves appear separately before and behind the obstacle, and, hence, the effect of viscosity on two typical kinds of waves can be analyzed. The linearized differential equation for the stream function is solved analytically to obtain the waveform. The calculated damping rate of wave amplitude does not agree well with that of Stokes’ approximate estimation. This shows that the Stokes’ estimation is not sufficient, and that an exact analysis as presented here is necessary when the Reynolds number is as low as Re≦ 1000. As an application of this analysis, the waveform is calculated for the stationary wave formed by an obstacle in falling liquid film flow.