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

For ${\mathbf{u}}_0=-\frac{3}{2}\Omega x{\mathbf{e}}_y$, advection and viscosity vanish, while its Coriolis acceleration cancels $-\nabla {\Phi }_t$; constant pressure and $\theta =0$ complete the equilibrium. For axisymmetric perturbations,