Chaotic particle transport in time-dependent Rayleigh-Bénard convection

Abstract

The transport of passive impurities in nearly two-dimensional, time-periodic Rayleigh-B\'enard 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.