 Double-diffusive overflow reservoir

A steady well-mixed hot salty reservoir receives volume flux $Q$ and loses the same flux over a weir. Heat and salt balances are $Q(T_i-T)=A{F}_T$ and $Q(S_i-S)=A{F}_S$. If $\beta F_S/(\alpha F_T)=R_F$ and $\alpha F_T=b(\alpha \Delta T{)}^{4/3}/R_{\rho }^2$, define $R_0=\beta (S_i-S_{\infty })/[\alpha (T_i-T_{\infty })]$. Then ${\eta }_s=(R_F/R_0){\theta }_s$ and $C=Ab[\alpha (T_i-T_{\infty }){]}^{1/3}/(Q{R}_0^2)$. For $R_0>1$ and $0\le R_F<1$ the interface is statically stable while preferential heat transfer can drive double-diffusive convection.