Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 321 / 3 / e / Solution

For $\nu =0$,An exponentially growing root exists exactly when $1+n^2<0$, orThus an adverse radial entropy gradient $N^2<0$ must overcome the epicyclic restoring effect of rotation. Rotation stabilizes gradients with $-{\Omega }^2<N^2<0$.