FRACTIONAL BROWNIAN-MOTION OF PARTICLES IN CAPILLARY WAVES

On the surface of a vertically oscillating fluid, capillary waves with a clearly discernible wavelength lambda are formed if the amplitude o f the oscillations exceeds a critical value, Particles sprinkled on th e fluid surface are experimentally found to move in an almost Brownian motion when measured over distances larger than lambda. We extend ear lier studies of the diffusivity to length scales ranging from 0.1 lamb da to 10 lambda. We observe a cross-over in the diffusive motion from a strongly anomalous diffusion below lambda to a motion that is closer to bring Brownian above lambda, Our observations show that the partic le motion is well described by an amplitude-independent fractional Bro wnian motion effective at sizes less than lambda, convoluted with an a mplitude-dependent fractional Brownian motion, effective on all length scales smaller than the system size. At large amplitudes our results are in surprising agreement with diffusivity measurements from upper-o cean studies.