Fractal drifter trajectories in the Kuroshio extension

We study the fractal and scaling properties of the Lagrangian trajectories of three satellite-tracked, freely drifting buoys (drifters) placed in the Kuroshio extension region during 1977. Over a period of about one year, the drifters, whose positions followed approximately the motions of fluid parcels in the near-surface layer, traveled almost the entire width of the Pacific Ocean. During this time, the drifters followed what may be described as highly erratic paths, while on the average being advected eastward in the zonal flow. Here we apply four different data analysis methods, based on the mathematics of fractals, to the drifter paths. We find that for space scales extending from at least 20 to 150 km and time scales from 1.5 days to 1 week, each of the trajectories displays fractal and scaling behavior with a fractal dimension of approximately 1.3. The multifractal nature of the drifter trajectories is also explored. The implication of these results is that the near-surface Lagrangian mesoscale motions in the Kuroshio Extension exhibit fractal properties in a range of scales normally attributed to geophysical fluid dynamical turbulence. These results evidently provide the first experimental evidence that fluid parcel trajectories in large-scale ocean flows can exhibit fractal behavior. A relation between the observed value of the fractal dimension and the properties of the power spectrum of a typical drifter position coordinate is also exploited. We finally discuss some of the possible physical implications of these results for the study of geophysical fluid dynamical flows.