= Post-shutdown double-diffusive reservoir cooling
{title2=$\eta=q\theta,\quad q=R_F/R_0$}
After inflow and overflow cease, a fixed-volume reservoir initially in the preceding steady state obeys $\eta=q\theta$ and $\dot\theta=k(1-\theta)^{10/3}/(1-q\theta)^2$, with $k=Ab[\alpha(T_i-T_\infty)]^{1/3}/(V R_0^2)$. Integrating gives $k(t-t_0)=G(\theta)-G(\theta_s)$, where $G=3(1-q)^2(1-\theta)^{-7/3}/7+3q(1-q)(1-\theta)^{-4/3}/2+3q^2(1-\theta)^{-1/3}$. For $q<1$, heat contrast tends to zero only at infinite time, while a nonzero salt contrast remains.
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