  We test the ability of a low-dimensional turbulence model to predict how
dynamics of large-scale coherent structures such as convection rolls change in
different cell geometries. We performed Rayleigh-B\'enard convection
experiments in a cubic container, in which there is a single convection roll
known as the large-scale circulation (LSC). The model describes the motion of
the orientation $\theta_0$ of the LSC as diffusion in a potential which is
predicted as a function of the shape of the cell from an approximate solutions
of the Navier-Stokes equations. The model predicts advected oscillation modes,
driven by a restoring force created by the non-circular cell cross-section. We
observe the predicted lowest-wavenumber mode in which the LSC orientation
$\theta_0$ oscillates around a corner, and a slosh angle $\alpha$ rocks back
and forth, which is distinct from the higher-wavenumber advected twisting and
sloshing oscillations found in cylindrical cells. The potential has quadratic
minima near each corner with the same curvature in both the LSC orientation
$\theta_0$ and slosh angle $\alpha$, as predicted. The new oscillation mode
around corners is found above a critical Ra $=4\times10^8$, which appears in
the model as a crossing of an underdamped-overdamped transition. The natural
frequency of the potential, oscillation period, power spectrum, and critical Ra
for oscillations are all within a factor of 3 of model predictions for the
Rayleigh number range $8\times10^7 \le Ra \le 3\times 10^9$. However, these
uncertainties in model parameters are too large to correctly predict whether
the system is in the underdamped or overdamped state at a given Ra. The success
of the model at predicting the potential and flow modes for a cubic cell
suggests that such a modeling approach could be applied more generally to
different cell geometries that support a single convection roll.
