 Solution

The unperturbed fluid wake is the horizontal strip $-h<y<h$: the fluid is stationary there and moves to the right with velocity $U{\mathbf{e}}_x$ above and below it. Its two shear layers are the straight lines $y=\pm h$. After the symmetric disturbance, draw the upper layer at $y=h+\eta (x,t)$ and the lower one as its reflection at $y=-h-\eta (x,t)$, so the local wake width is $2(h+\eta )$.