= Stationary neutral curve of rotating convection
{title2=$R_s=[(k^2+n^2\pi^2)^3+\mathrm{Ta}\,n^2\pi^2]/k^2$}
Substitution of zero growth rate into the rotating-convection cubic gives the displayed <Rayleigh number>. For the first vertical mode, setting $t=k^2$, $m=\pi^2$, differentiating with respect to $t$ gives $(t+m)^2(2t-m)=\mathrm{Ta}\,m$. At rapid rotation, $k_c\sim(\mathrm{Ta}\pi^2/2)^{1/6}$ and $R_c\sim3(\mathrm{Ta}\pi^2/2)^{2/3}$. Discrete allowed <wavenumbers> or different plate conditions require a different minimization.
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