Taylor–Couette flow is a flow between two rotating, infinitely long, coaxial cylinders. The original problem was solved by Stokes in 1845, but Geoffrey Ingram Taylor's name was attached to the flow because he studied its stability in a famous 1923 paper.
The problem can be solved in cylindrical coordinates . Denote the radii of the inner and outer cylinders as  and . Assuming the cylinders rotate at constant angular velocities  and , then the velocity in the -direction is
This equation shows that the effects of curvature no longer allow for constant shear in the flow domain.