Solution
= Solution
The radial strain draws fluid inward, axial strain expels it away from the midplane, and $v(r)$ supplies swirl. In cylindrical coordinates $r^{-1}\partial_r(r(-αr))+\partial_z(2αz)=-2α+2α=0$, so the flow is incompressible.
= Solution
The radial strain draws fluid inward, axial strain expels it away from the midplane, and $v(r)$ supplies swirl. In cylindrical coordinates $r^{-1}\partial_r(r(-αr))+\partial_z(2αz)=-2α+2α=0$, so the flow is incompressible.