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We investigate the large-scale transport of inertial particles. We deriveexplicit analytic expressions for the eddy diffusivities for generic Stokestimes. These latter expressions are exact for any shear flow while theycorrespond to the leading contribution either in the deviation from the shearflow geometry or in the P\'eclet number of general random Gaussian velocityfields. Our explicit expressions allow us to investigate the role of inertiafor such a class of flows and to make exact links with the analogous transportproblem for tracer particles.

Eddy diffusivities of inertial particles in random Gaussian flows