  We study the motion of an inertial particle in a fractional Gaussian random
field. The motion of the particle is described by Newton's second law, where
the force is proportional to the difference between a background fluid velocity
and the particle velocity. The fluid velocity satisfies a linear stochastic
partial differential equation driven by an infinite-dimensional fractional
Brownian motion with arbitrary Hurst parameter H in (0,1). The usefulness of
such random velocity fields in simulations is that we can create random
velocity fields with desired statistical properties, thus generating artificial
images of realistic turbulent flows. This model captures also the clustering
phenomenon of preferential concentration, observed in real world and numerical
experiments, i.e. particles cluster in regions of low vorticity and high strain
rate. We prove almost sure existence and uniqueness of particle paths and give
sufficient conditions to rewrite this system as a random dynamical system with
a global random pullback attractor. Finally, we visualize the random attractor
through a numerical experiment.
