Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 331 / 3 / a / iii

For a temporally unstable base flow, the relevant saddle growth rate along a ray distinguishes two cases in the chosen observation frame:A convective hydrodynamic instability amplifies a travelling wave packet but lets a localized disturbance decay at any fixed point. An absolute hydrodynamic instability grows at a fixed point. The separating case $\sigma (0)=0$ is marginal in exponential rate and can have an algebraic prefactor. In a frame moving with $V$, replace $\sigma (0)$ by $\sigma (V)=\mathrm{Im}({\omega }_{\star }-V{k}_{\star })$: this distinction depends on the observation frame.