Simulation of homogeneous and incompressible Cinlar flows

We study the simulation of stationary, homogeneous, incompressible and isot ropic Cinlar flows on R-2. The flow is generated by a velocity field obtain ed by the superposition of vortices of rotation. The arrival time and locat ion of vortices form a Poisson point process. The two stages of the simulat ion of the flow are the generation of the velocity field and the integratio n of the particle paths. We generate the velocity held on a bounded domain D exactly. The velocity field on D is fully described by the parameters of vortices that are stored in a stack the size of which is fairly stable at t he stationary regime. We obtain the particle path by integrating the flow e quation using a fourth order Runge-Kutta method. A range of ratios of the t wo relevant time scales lead to a variety of particle paths. Under some reg imes, the paths are nearly Brownian, under other, the paths are clearly cir cular with some drift. Finally, we compute single particle dispersion, Lagr angian autocorrelation, and diffusivity estimators through Monte Carlo simu lations. The results are useful for fitting the model to real data. (C) 200 0 Elsevier Science Inc. All rights reserved.