ON PREDICTABILITY OF PARTICLE CLUSTERS IN A STOCHASTIC FLOW

Abstract

In many physical applications it is important to predict particle trajectories in a turbulent flow using a numerical model of the flow. One of the major reasons for a poor prediction is the limited resolution in space. We discuss the problem of predictability limits in the framework of a stochastic flow modeling inertial particles in turbulence. Two stochastic flows called the "model" and "true" are considered. The "model" flow is the "true" flow smoothed in space. The principal measure of discrepancy of the flows is the distance between the centers of mass of two initially identical particle clusters driven by the "true" and "model" flows respectively. The predictability limit is defined as a moment when this distance exceeds the space correlation scale of the true flow. The main result is a simple formula relating the predictability limit with the smoothing scale. This relation is well supported by stochastic simulations and could be a helpful tool in planning experiments in numerical models of turbulent flows. Also the difference between particle scattering in the "true" and "model" flows is studied.