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 dist inct length scale present in our experiment, namely, the wavelength la mbda of the surface waves. We observe non-Brownian particle trajectori es with a fractal dimension D different from the random walk value D = 2. A crossover is observed from one anomalous behavior at length scal es below lambda, to another at larger length scales. Data collapse is shown to be feasible, and scaling functions characterizing the crossov er are identified. Our results are compared to those obtained from obs ervations of drifters in the upper ocean. The distinct length scale la mbda allows us to divide the particle trajectories into flights and tr aps. The distribution of flight times shows a power-law behavior with an exponent between 2.3 and 3.