The adiabatic overturning circulation is the part of the meridional overturning circulation that persists in the limit of vanishing diffusivity. Two conditions are required for the existence of the adiabatic overturning circulation: a high-latitude zonally-reentrant channel subject to surface westerlies and a set of outcropping isopycnals which are shared between the channel and the opposite hemisphere. Freshwater forcing, applied as specified surface flux makes the salinity concentration, and thus the sea surface buoyancy (and the size of the shared isopycnal window) part of the solution. We find that a positive salt-advection feedback leads to a surface buoyancy distribution which increases the size of the isopycnal window and strengthens the adiabatic overturning circulation: the residual overturning circulation transports salt northward, compensating the decrease in buoyancy due to the northward temperature transport. The positive salt feedback can also lead to a solution with a reversed circulation, whereby water sinks north of the channel and upwells in the high latitudes of the northern hemisphere: unlike the forward cell, the reverse cell is diffusive and thus vanishes in the adiabatic limit. The transition between the two solutions is mediated by decadal and multicentennial oscillation, whose amplitude increases in the vicinity of the transition threshold. We speculate that increased variability is one of several indicators that can be used to anticipate transitions to a shut-down of the overturning circulation.