The Floquet Analysis of Liquid Interface Wave in a Double-Frequency Excited Cylindrical Container

Abstract

In generally cylindrical container, by the method of separation of variables solve the Laplace equation and linearized boundary conditions and obtain amplitude equation of double-frequency excitation fluid interface waves considering surface tension effects. We use double-layer single-frequency viscous fluid damping coefficient to modify the amplitude equation, and then analyze the instability of the new amplitude equation using Floquet theory. By numerical calculation, the instability region determined by different depths, excitation frequency, excitation amplitude, relatively amplitude factor, the phase difference and the surface tension is given. Moreover, the double-frequency excitation spectrum of double critical phenomena is also discussed.