On relative spatial diffusion in plasma and fluid turbulences: clumps, Richardson's law and intrinsic stochasticity

The relative diffusion of charged particles in turbulent electric fields exhibits different behaviours according to the time regime: t3, for short times (representing a reduction of diffusion due to trajectory correlations); exp (t), for intermediate times (due to trajectory renormalisation); t3 again, asymptotically, for long times (representing independent particle diffusion). The second regime corresponds to an exponential separation of neighbouring trajectories and a strong dependence on initial conditions, with non-zero Lyapunov exponent. However, this behaviour is due to an extrinsic stochasticity. Analogous regimes exist in problems of Brownian motion and neutral fluid turbulence. The appearance of an exponential behaviour is due to a failure of the quasilinear approximation for neighbouring particles. A similar situation exists in other classical problems of plasma kinetic theory.