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We examine thermal convection in a two-dimensional annulus using fullyresolved direct numerical simulation (DNS) in conjunction with alow-dimensional model deriving from Galerkin truncation of the governingNavier-Stokes Boussinesq (NSB) equations. The DNS is based on fast and accuratepseudo-spectral discretization of the full NSB system with implicit-explicittime stepping. Inspired by the numerical results, we propose a reduced modelthat is based on a Fourier-Laurent truncation of the NSB system and cangeneralize to any degree of accuracy. We demonstrate that the lowest-ordermodel capable of satisfying all boundary conditions on the annulus successfullycaptures reversals of the large-scale circulation (LSC) in certain regimes.Based on both the DNS and stability analysis of the reduced model, we identifya sequence of transitions between (i) a motionless conductive state, (ii) astate of steady circulation, (iii) non-periodic dynamics and chaotic reversalsof the LSC, (iv) a high Rayleigh-number state in which LSC reversals areperiodic despite turbulent fluctuations at the small scale. The reduced modelreveals a link to a damped pendulum system with a particular form of externalforcing. The oscillatory pendulum motion provides an accurate prediction forthe LSC reversal frequency in the high Rayleigh-number regime.

A convective fluid pendulum revealing states of order and chaos