Statistical properties of passive tracers in a positive
four-point vortex model
Abstract
Stochastic properties of systems formed by many passive
particles conducted by 4 point vortices, each one with positive
circulation, are investigated. A statistical
$\chi^2$ test is developped in order
to study the spatial distribution of particles in the chaotic
background $\lambda_{L}>0$. The fact that the
uniform distribution is an invariant measure of the spatial
distribution of particles is used to debug the
$\chi^2$ test. This procedure is
applied in the same conditions as described in Babiano et
al. in order to study the uniformity of passive
particles. It is observed that uniformity is not attained up to
times of order 105 n.t.u., when either a gaussian or
a uniform initial distribution is considered in a small region
away from the vortices.