Fractal particle trajectories in capillary waves: Imprint of wavelength

We examine particle trajectories in capillary waves formed on a water surface subject to vertical vibrations. We focus on the role of a distinct length scale present in our experiment, namely, the wavelength lambda of the surface waves. We observe non-Brownian particle trajectories with a fractal dimension D different from the random walk value D = 2. A crossover is observed from one anomalous behavior at length scales below lambda, to another at larger length scales. Data collapse is shown to be feasible, and scaling functions characterizing the crossover are identified. Our results are compared to those obtained from observations of drifters in the upper ocean. The distinct length scale lambda allows us to divide the particle trajectories into flights and traps. The distribution of flight times shows a power-law behavior with an exponent between 2.3 and 3.