Experimental Studies On Faraday Waves In A Hele-Shaw Cell

In practical applications,liquid sloshing caused by the vibration of large-scale equipments is a general physical phenomena,and it has various forms.The studies on this problem are essential for a wide range of industries,such as chemical engineering,oil exploitation,ship building and aerospace engineering.In a majority of previous studies on these topics,most work focuses on the dynamics and formation mechanism of the Faraday waves by theories,numerical simulations and experiments.This dissertation is devoted to study the resonance waves in a Hele-Shaw cell mainly by experiments.Some families of Faraday waves are observed,and the properties and dynamics of them are investigated experimentally.Three typical problems are studied in details and described briefly as follows:(1)Two types of stable,highly localized Faraday resonant standing waves with multiple crests and troughs are observed in a Hele-Shaw cell partly filled with the ethanol-water solution vertically oscillated with a single frequency.Systematical experiments are performed to investigate the properties of these oscillons.It is found that the wave height of these oscillons is independent of fluid depth from1 to 5 cm.With other parameters fixed,the average wave height increases with the forcing acceleration amplitude,and there are the upper and lower thresholds of the forcing acceleration.A similar window of acceleration amplitude exists for forcing frequency selection.In particular,some experiments are performed to indicate the high localization of the oscillons,which suggests that these oscillons may be regarded as a combination of the two elementary oscillons.(2)A family of two-dimensional Faraday waves in extremely shallow depth(D ?2mm)of pure ethanol are observed experimentally in a Hele-Shaw cell that oscillates vertically.These waves have strong nonlinearity.Systematical experiments are performed to study these waves,and it is found that the wave height increases with the forcing acceleration amplitude when other parameters are fixed.The pattern changes when the acceleration is over some threshold and there is hysteretic jump in the transitions.(3)A system of two-dimensional,two coupled Faraday interfacial waves is experimentally observed in the two layers(pure ethanol and silicon oil)in a sealed Hele-Shaw cell with periodic vertical vibration.The upper and lower Faraday waves coexist: the upper vibrates vertically,but the crests of the lower one oscillate horizontally with unchanged wave height.The systematical experiments are performed to study these two types of Faraday waves.It is found that the upper faraday waves will not be observed when the depth of the upper fluid is over some threshold.The wave height of the lower Faraday waves is a linear function(in the case of a fixed forcing frequency)or a parabolic function(in the case of a fixed acceleration amplitude)of that of the upper,with the same length.Besides,these results illustrate that the lower layer plays a role as a flexible boundary.In conclusion,we observe some families of two-dimensional Faraday waves in experiments.These phenomena are helpful to deepen and enrich our understandings about Faraday waves,and besides provide a challenging problem for both theories and computational fluid dynamics.