Are SOFAR Float Trajectories Chaotic?

Abstract

When particle trajectories in a fluid are chaotic, the fluid is stirred efficiently, which, in turn, enhances diffusive mixing within the fluid. Regular (nonchaotic) particle trajectories on the other hand, are not associated with efficient stirring. The question of whether or not SOFAR float trajectories are chaotic is, then, central to understanding the process by which passive tracers are laterally mixed in the ocean. Two techniques commonly used to investigate the behavior of computer generated trajectories, the construction of Poincaré sections and the calculation of Lyapunov exponents, cannot be applied to analyze isolated float trajectories in an unknown velocity field. Power spectra of both meridional and zonal components of float trajectories contain structure on all resolvable scales, suggesting chaotic motion. Attempts to estimate K2, a lower bound on the Kolmogorov entropy, using the Grassberger-Procaccia algorithm failed when individual trajectories were used as input. Using a multiple trajectory embedding technique, however, K2. was estimated using the same algorithm to be approximately (140 day)?1. This also suggests that the motion is chaotic. While our analysis does not unambiguously identify SOFAR float trajectories as being chaotic, it provides no evidence that the trajectories are not chaotic.