The complete cascade of bifurcations from steady to chaotic convection, as the Rayleigh number is varied, is considered numerically inside an air-filled differentially heated cavity. The system is assumed to be two-dimensional and is invariant under a generalized reflection about the center of the cavity. In the neighborhood of several codimension-two points, two main routes emerge, characterized by different symmetries of the first oscillatory eigenstate. Along these two competing routes, different sequences of bifurcations and symmetry breakings lead from the steady base flow to the hyperchaotic regime. Several families of two- and three-frequency tori have been identified via the computation of the leading Lyapunov exponents. Modal structures extracted from time series reveal the occurrence of slow internal oscillations in the center of the cavity and faster wall modes confined to vertical boundary layers. Further quasiperiodicity windows have been detected on each route. The different regimes eventually disappear in a boundary crisis in favor of a single, globally symmetric, hyperchaotic regime.

The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio 2 and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zones depending on whether the statistics of return times exhibit exponential or algebraic decay. Melnikov functions are computed and predict the appearance of the main mixing regions via the break-up of the homoclinic and heteroclinic orbits. The non-hyperbolic regions are characterised by a larger number of Kolmogorov-ArnoldMoser (KAM) tori. Based on the numerical extraction of many unstable periodic orbits (UPOs) and their stable/unstable manifolds, we suggest a coarse-graining procedure to estimate numerically the spatial fraction of chaos inside the cavity as a function of the Rayleigh number. Mixing is almost complete before the first transition to quasiperiodicity takes place. The algebraic mixing rate is estimated for tracers released from a localised source near the hot wall.