Exact results on the large-scale stochastic transport of inertial particles including the Basset history term

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.