Spatiotemporal characterization of interfacial Faraday waves by means of a light absorption technique

Abstract

We present measurements of the complete spatiotemporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a light absorption technique we are able to determine the bifurcation scenario from the flat surface to the patterned state for each complex spatial and temporal Fourier component separately. The surface spectra at onset are found to be in good agreement with the predictions from the linear stability analysis. For the nonlinear state our measurements show in a direct manner how energy is transferred from lower to higher harmonics and we quantify the nonlinear coupling coefficients. Furthermore we find that the nonlinear coupling generates static components in the temporal Fourier spectrum leading thus to a contribution of a nonoscillating permanent sinusoidal deformed surface state. A comparison of hexagonal and rectangular patterns reveals that spatial resonance can give rise to a spectrum that violates the temporal resonance conditions given by the weakly nonlinear theory.

Numerical simulation of two-dimensional Faraday waves with phase-field modelling

“…In nonlinear regimes, comparison with experimental data is crucial. Remarkably, the simulation result by Périnet, Juric & Tuckerman (2009) is in perfect agreement with the experimental data in the nonlinear regime conducted by Kityk, Embs, Mekhonoshin & Wagner (2005), where the top fluid's motion cannot be neglected.…”

“…These surprising findings would probably be outside of the applicable range of the weakly nonlinear theories, such as the one developed by Chen & Viñals (1999), on selection of various patterns of Faraday waves. Hence, to understand these phenomena, fully nonlinear numerical simulations of the Faraday systems, which can be complementary to laboratory experiments, play an indispensable role as discussed in Kityk, Embs, Mekhonoshin & Wagner (2005). Perhaps the first such simulation, in which the motions of both the top and bottom fluids are simultaneously simulated, was performed recently by Périnet, Juric & Tuckerman (2009).…”

Three-Dimensional Fluid Motion in Faraday Waves: Creation of Vorticity and Generation of Two-Dimensional Turbulence

“…Parametric surface waves can self-organize into various motifs and they have been the focus of the pattern formation physics for many years [11][12][13]. Stable patterns, crystals, or even quasi-crystals are produced on the surface of dissipative liquids [14][15][16] or granular media [17,18]. At higher wave amplitudes such patterns break down into disordered lattices.…”

Numerical simulation of Faraday waves

“…However, in contrast to the previously cited investigations, the numerical method described here solves the Navier-Stokes equations for the general case of two distinct superposed fluids. The capability of the method to simulate the motion of both fluids is important in that it permits comparison of numerical results with those of certain experimental configurations, namely those of Kityk et al (2005) where the lighter fluid cannot be ignored. These experiments were the first to provide quantitative measurements of the complete spatio-temporal Fourier spectrum of Faraday waves and thus form an excellent basis for quantitative comparison with our numerical results in the nonlinear finite amplitude regime, i.e.…”