理想流体的法拉第波模态

Vibrating modes of Faraday waves in ideal fluid

研究了理想流体的法拉第波模态.由法拉第波的振幅方程给出了稳定条件下的色散关系,利用参量共振方程得到了在亚简谐条件下本征波矢的取值范围.引入几何模型,在一定实验条件下,可以简单而直观地预测模态及其花纹图案.解释了不同模态的竞争情况,对比分析了相图关系的理论预测结果,几何模型的预测与实验及理论计算结果相符合.

The Faraday wave patterns and corresponding vibrating modes in ideal fluid were studied theoretically and experimentally.The dispersion relation had been got by deriving the amplitude equations of Faraday waves.The range of eigenvalue was also calculated based on the parametric resonance theory.To predict possible patterns in real space,ageometric model on the basis of experimental parameters was proposed,which could intuitively predict the different wave patterns and the conditions of mode competitions.The experimental phase diagram was also analyzed.A good agreement between the measured and theoretical results was obtained.