 Two-box overturning model

A reduced model with warm and cold mixed reservoirs whose signed exchange volume flux is proportional to their density difference. For fixed temperature contrast and reference-salinity freshwater forcing, the stationary salt budget is $|q|\Delta S=E{S}_0$. A linear equation of state then gives $q|q|-k\alpha \Delta T|q|+k\beta S_{0}E=0$. Positive circulation has two branches below a saddle-node bifurcation; the stronger positive branch and the reversed branch are stable under the usual salt budget dynamics.