Relative dispersion at the surface of the Gulf of Mexico

We examine the relative motion of pairs and triplets of surface drifters in the Gulf of Mexico. The mean square pair separations grow exponentially in time from the smallest resolved scale (1 km) to 40-50 km, with an e-folding time of 2-3 days. Thereafter, the dispersion exhibits a power law dependence on time with an exponent of between 2 and 3 (depending on the measure used) up to scales of several hundred kilometers. The straining is for the most part isotropic, with only weak regional variations. But there are suggestions of anisotropy in the western basin, probably due to boundary current advection. The pair velocities are correlated during the early phase and a portion of the late phase. The relative displacement distributions during the early phase are, after an initial adjustment, non-Gaussian and approximately constant, suggestive of local straining. The triplet results likewise suggest two growth phases. During the early phase, the mean area and the longest triangle leg grow exponentially in time, the latter with a rate consistent with the two-particle results. Most triangles are drawn out during this time. During the late period, the triangles grow and their aspect ratios systematically decrease, suggesting an evolution to an equilateral shape. Although surface divergences should affect these statistics, they nevertheless strongly resemble those found with two-dimensional turbulent flows. If so, we would infer an enstrophy cascade at scales below the deformation radius (40-50 km) which is probably spectrally local. The latter implies that growth in particle separations comes from flow features the same size as the separations. It is also possible there is an inverse energy cascade to scales larger than the deformation radius, driven possibly by baroclinic instability. However, the late period statistics may also reflect dispersion by a large scale shear. We do not resolve an upper bound on the late time power law growth (i.e. we do not observe an ultimate diffusive stage). This may reflect shear dispersion. But it may also stem from surface convergences which can cause long time particle correlations, as seen in recent numerical simulations of particles on a surface bounding an interior turbulent flow.