An important expression of the non-linear character of the ocean's meridional overturning circulation (MOC) is the scaling of its amplitude with the magnitude of the vertical mixing coefficient (diffusivity) of heat and salt. This paper extends recent work that indicated that the Atlantic and Pacific MOC exhibit different scaling behaviour. An idealized two-basin model configuration is used to study the meridional overturning circulation under restoring boundary conditions. In particular, the effects of wind forcing and the choice of the parametrization of lateral mixing are examined.
Without wind, the scaling is similar in the two basins and consistent with theoretical predictions, provided that the diffusivity is small enough. Towards higher diffusivities the scaling of the overturning diverges. With non-zero wind, the sensitivity is strongly determined by the choice of the lateral mixing scheme. In case of traditional horizontal diffusion, the scaling behaviour is asymmetric due to spurious diapycnal mixing. With the Gent-McWilliams parametrization, the scaling is symmetric for the lower range of diffusivities, where results agree partly with theoretical scaling relations. In all cases considered, the pycnocline depth has the same sensitivity to diffusivity in both basins, implying that there is no universally valid relation between overturning strength and pycnocline depth.