We report the results of a series of numerical simulations performed with the aim to describe the dispersion of heavy particles transported by sea waves. Recent studies investigated the interplay between the wave Stokes drift and the inertial character of negatively buoyant particles that, ultimately, yields an augmented settling velocity. Our interest is to investigate the possible occurrence of a Brownian regime that would allow for the definition of a diffusion coefficient. The velocity and acceleration auto-correlation functions and the corresponding integral time scales show that already at a very low Stokes number the particles behave very differently from the fluid. The main consequence is that an asymptotic diffusive regime is rarely observed, except as a transient regime or when the background random noise is comparable with the wave field velocities.

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