The fractal dimension of drifter trajectories and estimates of horizontal eddy-diffusivity

Abstract

We analyse drifter data from the Northeast Atlantic and find that single-particle motion has fractal dimension D = 1.28 ± 0.08 at scales 5 to 100 km. The single particle trajectories are modeled using fractional Brownian motion. Integral time scale is therefore shown to be a function of both the time between position fixes and the length of the total period the drifter was tracked. The variance (particle dispersion) grows as approximately t_3/2. The probability density function of single-particle velocity is observed to be leptokurtic, consistent with the fractional Brownian motion model. The present work reports two-particle trajectories with fractal dimension D = 1.3 for scales from 8 km to 150 km. The two-particle dispersion is modelled as accelerated fractional Brownian motion, in which speed becomes a function of time elapsed since the particles were very near to each other. The acceleration is chosen to be consistent with the patch variance growing as t_2.34. The dependence of relative velocity between pairs of drifters separated by a distance l, is observed to scale as l_0.3. This is consistent with the accelerated fractional Brownian motion model for two-particle motion. DOI: 10.1034/j.1600-0870.1991.t01-1-00008.x