RÉSUMÉ

One of the principal tools to tackle turbulent dispersion problems is the celebrated Taylor-Green-Kubo formula. By virtue of this formula, the rate of transport (i.e. the eddy diffusivity) of a tracer can be evaluated as the time integral of the fluid velocity auto-correlation function along the fluid trajectories. Here, we show that Taylor-Green-Kubo formula can be generalized to include external forces and other terms describing the inertia of the particles. This result therefore applies to determine the eddy diffusivity of inertial particles of any inertia. Afterwards, we will show a simple model where generalized Taylor-Green-Kubo formula yields the exact expression for the eddy diffusivity of inertial particles, regardless of their density and at any Stokes number. These general and exact results may open new scenarios in the field of turbulent dispersion of inertial particles, and closure modeling in the sea and in the atmosphere.