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Vibrated fluids : Faraday waves, cross-waves, and vibroequilibria
The behavior of vibrated fluids and, in particular, surface or interfacial instabilities, has been the subject of continued experimental and theoretical attention since Faraday’s seminal experiments in 1831. Both orientation and frequency are critical in determining the response of the fluid to excitation. Low frequencies are associated with sloshing while higher frequencies may generate Faraday waves or cross-waves, depending on whether the axis of vibration is perpendicular or parallel to the interface. In addition, high frequency vibrations are known to produce large scale reorientation of the fluid (vibroequilibria), an effect that becomes especially pronounced in the absence of gravity. The results of experimental and theoretical
investigations into the effect of vibrations on fluid interfaces are described and compared. Experiments utilize a dual-axis shaker configuration that permits two independent forcing frequencies, amplitudes, and phases to be varied. Theoretical results include an extension of the nonlinear Schrodinger equation models used to study cross-waves since Jones (JFM 138, 1984) that takes account of surface tension and inhomogeneous forcing. The fact that the distributed forcing term varies on the same lengthscale as the cross-wave modulation is crucial in explaining the experimental results.