Two-box overturning model (source code)

= Two-box overturning model
{title2=$q|q|-A|q|+BE=0$}

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 $|q|\Delta S=ES_0$. A linear <equation of state> then gives $q|q|-k\alpha\Delta T|q|+k\beta S_0E=0$. 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.