Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 321 / 2 / b / i / Solution

The linear term $-(3/2){\Omega }_{K}x{\mathbf{e}}_y$ is the local Keplerian shear in the shearing sheet. The remaining constantis the gas's azimuthal velocity relative to the local Keplerian frame. The outwardly decreasing midplane pressure found in part (a)(iii) makes the gas Sub-Keplerian, so