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

When $N=0$, the factorized relation is $s(D^2+{\varpi }^2)=0$, soThe oscillatory roots are inertial waves restored by rotation; viscosity leaves their leading oscillation frequency unchanged and damps their amplitude at rate $\nu k^2$. The zero root is the decoupled buoyancy-variable mode.