  In this paper we examine the interaction of convection, rotation and mean
flows in a thermal annulus. In this system mean flows are driven by
correlations induced by rotation leading to non-trivial Reynolds stresses. The
mean flows act back on the convective turbulence acting as a barrier to
transport. For this system we demonstrate that the Generalised Quasilinear
Approximation (GQL) (Marston et al 2016) may provide a much better
approximation to the complicated full nonlinear dynamics than the widely used
Quasilinear Approximation (QL). This result will enable the construction of
more accurate statistical theories for the description of geophysical and
astrophysical flows.
