The first two equations are horizontal momentum balances: local acceleration plus the <Coriolis acceleration> equals the pressure-gradient force. The third is linearized <mass conservation>: convergence raises the free surface, represented by $\phi$, while divergence lowers it. The constant $c$ is the long-wave gravity-wave speed.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 333 / 1 / i / Solution

 Solution (source code)