  Since the pioneering work of Richardson in 1926, later refined by Batchelor
and Obukhov in 1950, it is predicted that the rate of separation of pairs of
fluid elements in turbulent flows with initial separation at inertial scales,
grows ballistically first (Batchelor regime), before undergoing a transition
towards a super-diffusive regime where the mean-square separation grows as t^3
(Richardson regime). Richardson empirically interpreted this super-diffusive
regime in terms of a non-Fickian process with a scale dependent diffusion
coefficient (the celebrated Richardson's "4/3rd" law). However, the actual
physical mechanism at the origin of such a scale dependent diffusion
coefficient remains unclear. The present article proposes a simple physical
phenomenology for the time evolution of the mean square relative separation in
turbulent flows, based on a scale dependent ballistic scenario rather than a
scale dependent diffusive. This phenomenology accurately retrieves most of the
known features of relative dispersion ; among others : (i) it is quantitatively
consistent with recent numerical simulations and experiments (both for the
short term Batchelor regime and the long term Richardson regime, and for all
initial separations at inertial scales), (ii) it gives a simple physical
explanation of the origin of the super diffusive t^3 Richardson regime which
naturally builts itself as an iterative process of elementary
short-term-scale-dependent ballistic steps, (iii) it shows that the Richardson
constant is directly related to the Kolmogorov constant (and eventually to a
ballistic persistence parameter) and (iv) in a further extension of the
phenomenology, taking into account third order corrections, it robustly
describes the temporal asymmetry between forward and backward dispersion, with
an explicit connection to the cascade of energy flux across scales.
