In agreement with the numerical results from Plumb and Hou (1992), eddy-non-resolving (axisymmetric) simulations show that there exists a critical forcing amplitude at which the character of the forced flow changes from a linear, localized response to a non-linear, quasi angular momentum-conserving meridionally overturning response. The angular momentum-conserving nature of the supercritical response is evident in that the absolute vorticity is close to zero, and the angular momentum constant, at upper levels over and equatorward of the forcing region. As predicted by the nearly inviscid theory, the existence of a critical forcing amplitude is the manifestation of the dynamical constraint of zero absolute vorticity in the upper branch of the meridional circulation.
We investigate how this dynamical constraint of thermally forced overturning circulations is met when eddies are allowed to interact with the forced flow by performing 3D, eddy-resolving simulations with both zonally constant and zonally compact (localized both in longitude and in latitude) heating.