Symmetrical flow past an accelerated circular cylinder

The development of the two-dimensional flow of a viscous incompressible fluid around a circular cylinder which suddenly starts to move with the velocity U = U₀+U₁t+U₂t² is studied. Equations for the flow in terms of the stream function and vorticity in boundary-layer coordinates are presented. A perturbation series solution for small times is developed. The flow for longer times is computed numerically using an accurate implicit time-integration procedure. The numerical method is checked for small times by comparison with the results of the analytical solution. Reynolds numbers R in the range 200 to 10⁴ (based on the diameter of the cylinder) are considered. One particularly interesting result is that for certain values of U₁ and U₂ at R = 500 and R = 10³ it is found that two co-rotating vortices and three co-rotating vortices develop with time in each half of the wake in the two respective cases.