Absorbing processes in Richardson diffusion: analytical results

Details Absorbing processes in Richardson diffusion: analytical results Absorbing processes in Richardson diffusion: analytical results

2006-02-07

arxiv.org/abs/nlin/0602013v1

Physics of Fluids 18(048104), 2006

Nonlinear Sciences

Chaotic Dynamics

6 pages, 3 figures, sunbmitted to Physics of Fluids

Scientific paper

10.1063/1.2194969

We consider the recently addressed problem of a passive particle (a predator), being the center of a ``sphere of interception'' of radius $R$ and able to absorb other passive particles (the preys) entering into the sphere. Assuming that all the particles are advected by a turbulent flow and that, in particular, the Richardson equation properly describes the relative dispersion, we calculate an analytical expression for the flux into the sphere as a function of time, assuming an initial constant density of preys outside the sphere. In the same framework, we show that the distribution of times of first passage into the sphere has a $t^{-5/2}$ power law tail, seen in contrast to the $t^{-3/2}$ appearing in standard 3D diffusion. We also discuss the correction due to the integral length scale on the results in the stationary case.

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