  We introduce a low-order dynamical system to describe thermal convection in
an annular domain. The model derives systematically from a Fourier-Laurent
truncation of the governing Navier-Stokes Boussinesq equations and accounts for
spatial dependence of the flow and temperature fields. Comparison with
fully-resolved direct numerical simulations (DNS) shows that the model captures
parameter bifurcations and reversals of the large-scale circulation (LSC),
including states of (i) steady circulating flow, (ii) chaotic LSC reversals,
and (iii) periodic LSC reversals. Casting the system in terms of the fluid's
angular momentum and center of mass (CoM) reveals equivalence to a damped
pendulum with forcing that raises the CoM above the fulcrum. This formulation
offers a transparent mechanism for LSC reversals, namely the inertial overshoot
of a forced pendulum, and it yields an explicit formula for the frequency $f^*$
of regular LSC reversals in the high Rayleigh-number limit. This formula is
shown to be in excellent agreement with DNS and produces the scaling law $f^*
\sim Ra^{0.5}$.
