Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 334 / 1 / d / Solution

The wall is stationary in the laboratory and moves with velocity $+U{\mathbf{e}}_x$ in the sheet frame. Its no-slip boundary condition is thereforeThe first equation prescribes wall tangential velocity; the second imposes zero normal velocity. The streamfunction may have a constant mean value on the wall, set by the fluid transport, and that constant need not equal its value at the sheet.