  A stochastic version of the two-layer quasi-geostrophic model (2LQG) with
multiplicative transport noise is analysed. This popular intermediate
complexity model describes large scale atmosphere and ocean dynamics at the
mid-latitudes. The transport noise, which acts on both layers, accounts for the
unresolved small scales. After establishing the well-posedness of the perturbed
equations, we show that, under a suitable scaling of the noise, the solutions
converge to the deterministic 2LQG model with enhanced dissipation. Moreover,
these solutions converge to the deterministic stationary ones on the long time
horizon.
