The plastic particles are transported by the wind-driven surface currents of the ocean. In some regions, these currents converge. A fraction of the water sinks down to greater depths, while the light plastic particles remain at the ocean surface and eventually accumulate.

In other regions, the surface currents diverge, which means that more water is transported away from a region than is transported into the region. This has to be balanced by water from the deeper ocean layers coming to the surface. In these regions, the particle concentration will quickly decrease. This can be observed in the first few years of experiment 1 at the equator.

The simulations were carried out with the Max Planck Institute for Meteorology ocean model (MPI-OM TP04). Plastic particles were implemented as a tracer confined to the surface layer of the ocean.

Experiment 1

In the beginning, the particle concentration is uniformly distributed over all ocean basins with an initial concentration of one particle per square meter.

Experiment 2

In this experiment, the particles are only distributed along the coastlines in the beginning. The initial concentration is set to 1 particle per square meter as well. Due to the smaller total amount of particles in the ocean compared to the first experiment, the maximum values of the color scale are much smaller.

In both experiments, the plastic waste quickly accumulates in east-west-oriented bands. Over the years, these bands evolve into relatively small "garbage patches". The position of these patches depends only on the ocean currents; therefore the development is similar in both experiments.   
For further background information see, e.g., Wikipedia article Great Pacific garbage patch.