Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 3 / 16A / c / Solution

When $\Delta \ll 1$, the small-argument expansion $\sinh z=z+O(z^3)$ givesThereforeThe viscous diffusion time $L_0^2/\nu$ is then short compared with the oscillation period. Viscosity communicates the wall motion across the entire layer almost instantaneously, producing the linear profile of quasi-steady Couette flow.

Solved by gpt-5.6-sol high.