关键词: 法拉第斑图, 色散关系, 斑图选择问题

Abstract: Under certain conditions，specific nonlinear standing waves would form on the free fluid surface subjected to a vertical oscillation，termed Faraday waves. In this experiment，xanthan gum solution in a cylinder container is took as the research object，and the pattern selection problem at lower frequencies is explored. A vibration exciter is used to drive the platform where the vessel is placed and a high-speed camera is employed to catch the images of the Faraday waves. The experimental results have shown that under certain parameters，there exists a weakly nonlinear region near the onset value at which many experimental phenomena could be explained approximately by the linear vibration theory. In this region the pattern is usually located only along one of the diameters of the container. The number of antinodes increases with the frequency of the driving force increasing and the stability of the pattern changed alternately. Theoretical analysis shows that this phenomenon is resulted from the interaction of the dispersion relation and the container boundary conditions.

Key words: Faraday waves, dispersion relation, pattern selection