  Ergodic properties of a stochastic medium complexity model for atmosphere and
ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic
model for geophysical flows is studied, with the upper layer being perturbed by
additive noise. This model is popular in the geosciences, for instance to study
the effects of a stochastic wind forcing on the ocean. A rigorous mathematical
analysis however meets with the challenge that in the model under study, the
noise configuration is spatially degenerate as the stochastic forcing acts only
on the top layer. Exponential convergence of solutions laws to the invariant
measure is established, implying a spectral gap of the associated Markov
semigroup on a space of H\"older continuous functions. The approach provides a
general framework for generalised coupling techniques suitable for applications
to dissipative SPDEs. In case of the two-layer quasi-geostrophic model, the
results require the second layer to obey a certain passivity condition.
