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.