Steady streaming around a rotary oscillating circular cylinder in a uniform flow

The steady secondary flow around a circular cylinder oscillating rotationally about its axis in a uniform flow is investigated with the successive approximation based on the Oseen approximation. The equations for the secondary flow are derived analytically. Numerical solutions to these equations are obtained by using the solutions to the Oseen equations. It is shown that the steady streaming directs to the upstream and that the fluid velocity becomes slow as the frequency of the oscillation is increased. The drag due to the steady streaming is also obtained from numerical results and shown to take negative values at high frequencies of oscillation.