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The temporal development of two-dimensional viscous incompressible flow induced by an impulsively started circular cylinder which performs time-dependent rotational oscillations about its axis and translates at right angles to this axis is investigated. The investigation is based on the solutions of the unsteady Navier-Stokes equations. A series expansion for small times is developed. The Navier-Stokes equations are also integrated by a spectral-finite difference method for moderate values of time for both moderate and high Reynolds numbers. The numerical method is checked with the results of the analytical solution. The effects of the Reynolds number and of the forcing Strouhal number S on the laminar asymmetric flow structure in the near-wake region are studied. The lift and drag coefficients are also extracted from numerical results. An interesting phenomenon has been observed both in the flow patterns and in the behaviour of drag coefficients for S = π/2 at Reynolds number R = 500 and is discussed. For comparison purposes the start-up flow is determined numerically at a low Reynolds number and is found to be in good agreement with previous experimental predictions.

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The transient flow field caused by an infinitely long circular cylinder placed in an unbounded viscous fluid oscillating in a direction normal to the cylinder axis, which is at rest, is considered. The flow is assumed to be started suddenly from rest and to remain symmetrical about the direction of motion. The method of solution is based on an accurate procedure for integrating the unsteady Navier–Stokes equations numerically. The numerical method has been carried out for large values of time for both moderate and high Reynolds numbers. The effects of the Reynolds number and of the Strouhal number on the laminar symmetric wake evolution are studied and compared with previous numerical and experimental results. The time variation of the drag coefficients is also presented and compared with an inviscid flow solution for the same problem. The comparison between viscous and inviscid flow results shows a better agreement for higher values of Reynolds and a Strouhal numbers. The mean flow for large times is calculated and is found to be in good agreement with previous predictions based on boundary-layer theory.