Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 331 / 1 / e

At stationary onset, $\mu =0$. The lowest stress-free vertical mode is $\hat{W}=\sin \pi z$, for which $D^2=-{\pi }^2$ and ${\hat{D}}^2=-({\pi }^2+k^2)$. Substitution givesThe rotation term is positive, so rotation raises the critical Rayleigh number and is stabilizing.