Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 345 / 2 / b / Solution

Define the reduced gravityand use the Boussinesq limit ${\rho }_1\simeq {\rho }_2$ except in buoyancy. The balances becomeThus, for $\mathbf{q}=(g^{\prime },h,u{)}^T$,which is the required entraining shallow-water layer system.