Reversals of the large-scale circulation in thermal convection

The large-scale circulation (LSC) associated with thermal convection is known to spontaneously reverse direction. In the atmosphere, reversals can result in a sudden change in wind direction, while in the mantle, reversals may play a role in magnetic dipole shifts. We examine LSC reversals within the context of thermal convection in an annular domain. Through comparison with direct numerical simulations, we show that a low-dimensional dynamical system derived systematically from Galerkin truncation of the governing equations accurately describes a sequence of parameter bifurcations, including the onset of circulatory flow, the appearance of chaotic LSC reversals, and finally a high-Rayleigh-number state of periodic LSC reversals with small-scale turbulence. When cast in terms of the fluid's angular momentum and center of mass, the model reveals equivalence to a pendulum system with driving term that raises the center of mass above the fulcrum. It is the competition between driving, restoring, and damping that leads to the range of convective states. This physical picture yields accurate predictions for the frequency of regular LSC reversals in the high Rayleigh-number limit and offers a transparent mechanism for reversals.