= Lorenz model of thermosolutal convection
{c}
{title2=$a,b,c,d,e$}
A five-mode <Galerkin method> model retains the roll velocity $a$, its correlated temperature and concentration modes $b,d$, and the mean-profile distortions $c,e$. Its parameters include the <Prandtl number> $\sigma$, diffusivity ratio $\tau$, thermal forcing $r$, stabilizing solutal forcing $r_s$, and a positive geometric decay ratio $\varpi$. The velocity equation is $\dot a=\sigma(-a+rb-r_sd)$, while the scalar equations are $\dot b=-b+a(1-c)$, $\dot c=\varpi(-c+ab)$, $\dot d=-\tau d+a(1-e)$ and $\dot e=\varpi(-\tau e+ad)$. The solutal forcing is normalized using the thermal diffusion scale, so its steady stabilizing effect is $r_s/\tau$.
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