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

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-321/3/e/solution