Streamwise Oscillations of a Cylinder in Steady Current: Simulation of Long Wave Interaction with a Stationary Cylinder : Part B

Streamwise oscillations of a cylinder in steady current: simulation of long wave interaction with a stationary cylinder. In analogy with the well-known occurrence of locked-on vortex formation from a transversely-oscillating cylinder, patterns of locked-on vortices can occur from a cylinder oscillating in the streamwise direction. In this case, however, the patterns and thereby the loading are not at a single frequency. Rather, complex amplitude- and frequency-modulated, yet locked-on, vortex formation and fluctuating forces are attainable; correspondingly, the spectra of the cylinder loading exhibit a number of sharply defined peaks over a wide range of frequencies. In fact, the spectral component at the cylinder oscillation frequency may be substantially attenuated or suppressed. For the sinusoidal oscillation of the cylinder defined in the schematic, the instantaneous trace of the transverse force coefficient C_y exhibits a strongly distorted signature: a pronounced negative, then positive peak, followed by a region of small C_y. These pronounced negative and positive peaks correspond to the images N = 4 and 7, for which the cylinder is moving against the current. Over the time span between these two successive images, the initially-formed concentration of vorticity switches from the bottom to the top surface of the cylinder. In contrast, for images N = 14 and 17, over the same time increment as the foregoing, the movement of the cylinder in the same direction as the current results in a nearly "frozen" pattern of vorticity concentrations in the near-wake, i.e. the initially-formed vortex remains from the lower side of the cylinder. Moreover, on the right side of both of these images, interspersed small-scale concentrations of positive and negative vorticity are evident; they are due to out-of-plane, three-dimensional distortion of previously-formed vorticity concentrations. Dimensionless frequency and amplitude of the oscillation are f_e/f₀=0.44 and A/D = 0.955; f₀ is the K<rm<n frequency of the vertex formation from the corresponding stationary cylinder.