= Ice-bearing wall-plume thermodynamic invariant
{title2=$\phi Q\simeq(-E-c_pmS)/(L+c_pmC_0)$}
An ice-bearing plume at local liquidus equilibrium conserves excess enthalpy $E$ and salt $S$ relative to the ambient liquidus water. Eliminating its temperature and brine composition gives $\phi Q[L+c_pmC_0-L\phi]=-E-c_pmS+E\phi$. To dilute-crystal order this fixes its advected ice volume, hence its leading buoyancy flux. A positive rising branch needs a positive source invariant.
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