Unravelling the non homogeneous dispersion processes in coastal circulations using a clustering approach

Ocean and coastal circulations develop in complex domains, especially along the shorelines, and they are driven by forces with typical spatial and temporal distributions. The resulting flow is turbulent in character and inherits the inhomogeneities from the generating forces. When we come to study how these chaotic circulations transport mass, we must expect that the associated dispersion is equally turbulent and high variable in time and space. Observations of particle paths taught us how the trajectories could be complicated, often showing looping behaviours generated by different mechanisms (macro-vortices or periodicity in the flow). Despite this complexity, many available studies on ocean and coastal dispersion relies on considering the process as homogeneous (no variations in space) and applying different spatial and temporal averages, trying to grasp the overall picture of the dispersion.We propose a new approach that combines the fundamentals of the dispersion theories, i.e., autocorrelation functions, with an automated algorithm for clustering. We show that this approach is able to retain the highly inhomogeneous character of the ocean dispersion, at the same time, showing the physical link between the circulations and its ability to transport mass. A new mathematical model is also proposed to describe the different autocorrelations functions.