A Simple Prediction Algorithm for the Lagrangian Motion in Two-Dimensional Turbulent Flows

A new algorithm is suggested for prediction of a Lagrangian particle position in a stochastic flow, given observations of other particles. The algorithm is based on linearization of the motion equations and appears to be efficient for an initial tight cluster and small prediction time. A theoretical error analysis is given for the Brownian flow and a stochastic flow with memory. The asymptotic formulas are compared with simulation results to establish their applicability limits. Monte Carlo simulations are carried out to compare the new algorithm with two others: the center-of-mass prediction and a Kaiman filter-type method. The algorithm is also tested on real data in the tropical Pacific.