Instability analysis for Faraday waves under arbitrarily periodic vibration

In the framework of linear theory of instability the pattern instability is studied for a layer of a viscous fluid in a large aspect ratio container subject to vertically arbitrarily periodic excitation. As some applications, first the instabilities for Faraday water-wave system under excitations of the triangle and square waves are analyzed. Then, the relations between relative amplitudes and phase of the excitation, and the response modes of the patterns are investigated in the double-frequency Faraday experiment. The results are satisfactory. Project supported by the National Basic Research Project of Nonlinear Science and the Natural Science Foundation of Zhejiang Province.