Transport by capillary waves. Part I. Particle trajectories

Abstract

The transport of particles on capillary waves generated by the Faraday instability is studied experimentally. The motion of a single particle on the fluid surface is determined over 4×104 wave periods by particle tracking. Erratic particle motion over large distances occurs even for small wave amplitudes, where the pattern is ordered, though spatially modulated. This implies that the wave field is accompanied by significant flows with velocities approximately 30 times smaller than the instantaneous local fluid velocities. The particle motion is characterized statistically. The displacements of the particle in the two orthogonal directions follow independent Gaussian distributions. It is found that the variance of the particle’s displacement grows with the elapsed time interval as V(τ)∼τ2H over times long compared with the correlation time of the motion. The exponent H depends on the wave amplitude, decreasing gradually from about 0.7 to an asymptotic value of 0.5 (corresponding to classical Brownian motion) at large wave amplitudes.