Random renormalization groups and Bayesian scaling of dispersion/diffusion in Lake Michigan and the Gulf of Mexico

A random renormalization group technique and a related set of Bayesian scaling techniques are presented. The techniques are employed to study the motion of drifters in Lake Michigan on a time scale ranging from 30 minutes to 5 days, and in the Gulf of Mexico on a time scale ranging from 8 hours to 85 days. The scaling laws generalize the standard power-law scaling. One of the advantages of the Bayesian approach is that scaling laws can be determined even with a paucity of data with the caveat that less data produces greater uncertainty in the scaling laws.