Influence of uneven wall changing over time on the characteristics of liquid surface wave evolution

Abstract

This paper mainly studied the evolution of liquid surface waves along an uneven wall. Considering the characteristic of the uneven wall changing over time, the perturbation equation for the surface waves is derived by using the small parameter perturbation method to solve the control equations under the given boundary conditions. The method of derivative expansion is used to find the solution to the equation and numerical research is then carried out for the wall shape of a simple harmonic. By studying the influence of different parameters on the wavy wall, it can be found that when the frequency of the wall is small, the wavelengths of static waves and traveling waves are close to each other, promoting the merger between the surface waves, and the surface wave amplitude is obviously increased when the wall frequency and wall depth or Re increase. By contrast of the two cases of wavy wall and uneven wall, the surface wave on uneven wall has a periodical change at the same location with the increase of time, while the surface wave on wavy wall has an almost periodic change with a longer wavelength. Although the decrease of the wall amplitude and the wall frequency both can cause surface wave amplitudes reduced, the surface waveforms are different, for the surface wave on the wavy wall can be regarded as the superposition of wavy wall waveform and surface waveform caused by uneven wall.