Sensitivity of two-dimensional flow past transversely oscillating cylinder to streamwise cylinder oscillations

In this paper we study the sensitivity of flow past a transversely oscillating cylinder to streamwise harmonic perturbations. The value of the Reynolds number is equal to 150, for which the flow is two-dimensional. We start with a transversely oscillating cylinder and then impose a small streamwise (in-line) perturbation with a frequency equal to twice the transverse oscillation frequency. The cylinder is thus following an eight-shaped trajectory, which can be traversed in a counter-clockwise or clockwise direction. For low values of the in-line amplitude, we find for the counter-clockwise mode that the power transfer from the fluid to the structure increases with the amplitude of oscillation in the streamwise direction, even though the magnitude of the fluctuations of the forces is decreased. For the clockwise mode of motion we observe the reverse trend, i.e., the power transfer from the fluid to the structure is decreased, even though the magnitude of the fluctuations of the forces is increased. It is shown that the variation of the power transfer in both types of motion is due primarily to the variation of the phase between the transverse oscillation of the cylinder and the vortex lift force as a result of the in-line oscillation. For higher values of the streamwise amplitude, the contribution of the fluctuating drag to the power transfer also becomes important, especially for the counter-clockwise mode. Both modes of oscillation are characterized by the presence of the third harmonic in the spectrum of the lift force as the in-line oscillation is increased and by the appearance of a combination of single vortices on the one side of the wake, and vortex pairs on the other side.