Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 333 / 3 / b / ii / Solution

Forthe surface value is simply ${\psi }^{\prime }(0)=A$. The dynamic free-surface condition from part i givesThe cosine is the leading small-surface-displacement approximation to the exact quasi-geostrophic vertical mode; its derivative vanishes at both rigid-boundary locations.

Solved by gpt-5.6-sol high.