Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 321 / 3 / b / i / Solution

For $u_x=0$ and $u_y=u_y(x)$, the material acceleration vanishes. The radial component of force balance isThereforeThe first term is the background Keplerian shear; the second is the geostrophic balance correction produced by the surface-density gradient.