Duality of diffusion dynamics in particle motion in soft-mode turbulence.

Nonthermal Brownian motion is investigated experimentally by injecting a particle into soft-mode turbulence (SMT), in the electroconvection of a nematic liquid crystal. It is clarified that the particle motion can be classified into two phases: fast motion, where particles move with the local convective flow, and slow motion, where they are carried by global slow pattern dynamics. We propose a simplified model to clarify the mechanism of the short-time and asymptotic behavior of diffusion. In our model, the correlation time is estimated as a function of a control parameter ɛ. The scaling of the SMT pattern correlation time, τ(d)∼ɛ(-1), is estimated from the particle dynamics, which is consistent with a previous report observed from the Eulerian viewpoint. The origin of the non-Gaussian distribution of the displacement in the short-time regime is also discussed and an analytical curve is introduced that quantitatively agrees with the experimental data. Our results clearly illustrate the characteristics of diffusive motion in SMT, which are considerably different from the conventional Brownian motion.