Non-Hyperbolic Transport in Confined Oscillatory Convection

Abstract

The transport of passive tracers inside a two-dimensional differentially heated cavity is investigated numerically in the oscillatory regime, both in the vicinity and far from the corresponding Hopf bifurcation. Differential transport at low Rayleigh number is essentially linked to the exchange of fluid between two symmetric homoclinic tangles. A hierarchy of models is developed for the transient homogenisation process, the third order model reproducing well the observed behaviour. The vertical transport is efficient only at higher values of the Rayleigh number once all invariant tori have resonated. Signatures of non-hyperbolicity are shown by monitoring the variance of the coarse-grained concentration vs. time.