Dynamic mode decomposition based analysis of flow past a transversely oscillating cylinder.

Three-dimensional numerical computations are carried out for a cylinder undergoing controlled sinusoidal oscillation perpendicular to the free stream. The results are examined for Re = 500 and an oscillation amplitude of A / D = 0.25 , to allow comparison with the two-dimensional study by Blackburn and Henderson [J. Fluid Mech. 385, 255–286 (1999)]. The dynamic response of the flow is investigated over a wide oscillation frequency range from 0.5fo to 1.5fo, with fo being the natural shedding frequency of the fixed cylinder. As the oscillation frequency passes through fo, the ubiquitous abrupt shift in the phase of vortex shedding is again observed. On either side of this shift, the wakes exhibit Kármán mode of shedding, in the absence of the mode switch. The hypothesis for the mechanism of phase shift proposed by Blackburn and Henderson [J. Fluid Mech. 385, 255–286 (1999)] is further examined by quantitatively measuring the flux of vorticity generated on the base of the cylinder. Unlike in two-dimensional flow, where hysteresis is found to be associated with four branches, in three-dimensional flow only two longer branches K1 and K2 are identified, which bring out a remarkably simplified bifurcation structure. Dynamic mode decomposition (DMD) and its sparsity-promoting variant are used to characterize the coherent modes that govern the dynamics of the flow, as well as their corresponding frequencies. For the non-synchronized case, a multitude of DMD modes must be retained to accurately approximate the original flow, while for the synchronized case, only four DMD modes suffice to guarantee a same performance loss. In addition, the DMD modes that have the most profound impact on the hysteresis of lift and drag fluctuations are identified by DMD reconstruction. [ABSTRACT FROM AUTHOR]