Abstract
Experiments on the transport of passive scalar tracers on capillary waves generated by the Faraday instability are presented. A spot of fluorescent dye is placed just below the fluid surface and the evolution of the dye concentration field is studied. Substantial transport is found over large distances, consistent with earlier observations of particle motion on the fluid surface. The time evolution of the radial distribution of impurity is characterized on a coarse-grained scale. At large driving amplitudes ε, where the wave pattern is time-dependent with only short-range spatial correlations, the diffusion may be described as a normal Brownian process. At lower ε, where the patterns are well ordered (but modulated), this approximation fails though there is still significant transport. For large ε, the isoconcentration contours are well described as fractals with a dimension that approaches 1.40±0.05 at long times. The scalar gradient field may be described as a multifractal. These results are surprisingly similar to those obtained for transport in turbulent shear flows.
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