Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 333 / 4 / iv / Solution

The sloping boundary exerts the pressure dragon the fluid. At generation this equals ${\rho }_0\overline{u^{\prime }{w}^{\prime }}$: the mountain supplies a negative vertical flux of horizontal momentum to the wave. Where the wave dissipates, convergence of that flux transfers the same westward momentum to the mean flow. A forcing that maintains the prescribed uniform basic current must supply the compensating eastward momentum.