Past exam of the mathematics course of the University of Cambridge 2023 ii Paper 4 38C a Solution Created 2026-09-24 Updated 2026-09-25
The unperturbed fluid wake is the horizontal strip : the fluid is stationary there and moves to the right with velocity above and below it. Its two shear layers are the straight lines . After the symmetric disturbance, draw the upper layer at and the lower one as its reflection at , so the local wake width is .
Shear flow 2026-10-05
A shear flow has a velocity field varying across adjacent fluid layers, giving a nonzero shear rate. A parallel example is , with vertical shear . Linear shear flow has constant shear, while a shear layer concentrates the velocity change in a narrow region.