Low-Reynolds-number flow around an impulsively started rotating and translating circular cylinder

This paper describes the two-dimensional unsteady low-Reynolds-number flow past an impulsively started rotating and translating circular cylinder. Invoking the vorticity equation, we first derive a system of two coupled integral equations that govern the stream function and a modified vorticity function. This system, singular in the low-Reynolds-number, is then asymptotically solved by using a singular perturbation method and introducing five regions in the space-time domain. The first-order solutions are found to linearly depend on the translating and rotating motions within each region. Because of its importance for applications, a special attention is paid to the lift coefficient C _L which results here from intricate interactions between rotation and translation. The obtained initial asymptotic behavior of C_L actually exhibits a l^-1/2 singularity and thereby differs from the prediction of Badr & Dennis¹; at moderate Reynolds numbers.