Simulation of homogeneous and incompressible Çinlar flows

Abstract

We study the simulation of stationary, homogeneous, incompressible and isotropic Cinlar flows on R-2. The flow is generated by a velocity field obtained by the superposition of vortices of rotation. The arrival time and location of vortices form a Poisson point process. The two stages of the simulation of the flow are the generation of the velocity field and the integration 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 the stationary regime. We obtain the particle path by integrating the flow equation using a fourth order Runge-Kutta method. A range of ratios of the two relevant time scales lead to a variety of particle paths. Under some regimes, the paths are nearly Brownian, under other, the paths are clearly circular with some drift. Finally, we compute single particle dispersion, Lagrangian autocorrelation, and diffusivity estimators through Monte Carlo simulations. The results are useful for fitting the model to real data.