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侧壁振动所产生的表面波

ON THE SURFACE WAVES GENERATED BY A VIBRATING SIDE WALL

  • 摘要: 侧壁振动所产生的小振幅表面波的理论问题是一个求解具有混合边界条件的Laplace方程的问题.我们在引入一新的变量后,将它化为一Dirichlet问题,及使用复变函数方法求解,得到计算表面波复速势的普遍式.使用它得到了侧壁的三种典型振动的复速度、自由面的鉛直位移,无限远的波幅及辐射功率等.在实验中,装置了两种测量表面波的设备,证明了小振幅波的理论结果并观测了大振幅表面波的一些现象.发现在壁的恒定振幅下,侧壁振动频率有一临界值,超过它表面波的频率成为侧壁振动频率的一半,我们称这种波为半频波.关于半频波还需要可靠的理论解释。

     

    Abstract: The method of functions of complex variable is used in solving the problem of small amplitude surface waves on water generated by a vibrating side wall, the general formula for the complex velocity is given, and three different types of wall vibrations are discussed in some detail.
    Two different methods were used for the measurements and recording of surface waves. The experimental results in the case of small amplitude agree well with theory. Some observation and recording were made with large amplitudes. Second subharmonic vibrations were observed in the surface waves when the driving frequency is above a certain critical value. This phenomenon is yet to be accounted for theoretically.

     

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