Two-Particle Dispersion in Weakly Turbulent Thermal Convection

We present results from a numerical study of particle dispersion in the weakly nonlinear regime of Rayleigh-B\'enard convection of a fluid with Prandtl number around unity, where bi-stability between ideal straight convection rolls and weak turbulence in the form of Spiral Defect Chaos exists. While Lagrangian pair statistics has become a common tool for studying fully developed turbulent flows at high Reynolds numbers, we show that key characteristics of mass transport can also be found in convection systems that show no or weak turbulence. Specifically, for short times, we find Richardson-like $t^3$ scaling of pair dispersion. We explain our findings quantitatively with a model that captures the interplay of advection and diffusion. For long times we observe diffusion-like dispersion of particles that becomes independent of the individual particles' stochastic movements. The spreading rate is found to depend on the degree of spatio-temporal chaos.