Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 4 / a / Solution

Taking the divergence of the linear Euler equation and defining the peculiar-velocity divergence $\theta =\nabla \cdot \mathbf{v}$ givesThe assumption of negligible vorticity ensures that this longitudinal variable captures the velocity perturbation relevant to scalar density growth.

Solved by gpt-5.6-sol high.