The fractal dimension of relative lagrangian motion

Abstract

14 clusters of drifters are studied to obtain the fractal dimension of relative trajectories between pairs of drifters. Averaging over all experiments, the relative trajectories have a fractal dimension of 1.3 over separation scales ranging from 10 m to 4000 m. The clusters were deployed in Lake Erie, the Atlantic Equatorial Undercurrent, and in coastal waters off the south shore of Long Island. The average fractal dimension was quite similar for groups of experiments in each of these 3 areas, but it fluctuates over a greater range (1.59 to 1.12) when we consider individual experiments. This and consideration of variation of the generalized fractal dimension for higher moments, raise the possibility that trajectories are multifractal. The estimates we obtain for fractal dimension of relative lagrangian motion should be regarded as first estimates, pending analysis of more substantial data sets.