Chaotic particle transport in time-dependent Rayleigh-Bénard convection

Abstract

The transport of passive impurities in nearly two-dimensional, time-periodic Rayleigh-Bénard convection is studied experimentally and numerically. The transport may be described as a one-dimensional diffusive process with a local effective diffusion constant $D^{\mathrm{*}}$(x) that is found to depend linearly on the local amplitude of the roll oscillation. The transport is independent of the molecular diffusion coefficient and is enhanced by 1–3 orders of magnitude over that for steady convective flows. The local amplitude of oscillation shows strong spatial variations, causing $D^{\mathrm{*}}$(x) to be highly nonuniform. Computer simulations of a simplified model show that the basic mechanism of transport is chaotic advection in the vicinity of oscillating roll boundaries. Numerical estimates of $D^{\mathrm{*}}$ are found to agree semiquantitatively with the experimental results. Chaotic advection is shown to provide a well-defined transition from the slow, diffusion-limited transport of time-independent cellular flows to the rapid transport of turbulent flows.