Dynamic mode decomposition analysis of the two-dimensional flow past two transversely in-phase oscillating cylinders in a tandem arrangement

The flow through tandem square cylinders was investigated at a Reynolds number of 100 for oscillation amplitudes A = 0.1D to 0.7D and gaps L = 2.0D, 5.0D, and 6.0D, where D is the width of the cylinders. A moving reference frame method combined with the spectral/hp element method was employed to simulate the two-dimensional flow in the lock-in regime. Fluid forces, vorticity fields, power spectrum density, and pressure distribution were first investigated. Since surface pressure is directly connected with fluid forces, pressure and velocity field were synchronously analyzed by employing optimal dynamic mode decomposition. An underlying link between fluid forces and coherence modes was then uncovered. The results reveal that the move-induced forces and flow structures strongly depend on gaps and amplitudes in the lock-in regime. With respect to the dynamic mode decomposition analysis, odd-order modes contribute to lift forces, while even-order modes result in drag forces. The flow structures are dominated by at most three modes; as the amplitude increases, the high-order mode energy increases, coinciding with corresponding power spectrum density results of forces. Typical 2S, 2P, and C(2S) wakes were observed for various gaps and two representative amplitudes (A/D = 0 and 0.7), and their dominant modes show distinctive differences that lead to different local pressure shapes on the cylinders. It is the combined effects of local mode shape and global mode energy that account for the change in fluid forces for various gaps and two oscillating amplitudes. Published under an exclusive license by AIP Publishing.

Automated summary

The flow characteristics of tandem square cylinders were investigated under specific parameter conditions through numerical simulation methods. The results showed that the flow structures and fluid forces are dependent on the oscillation amplitudes and gaps in the lock-in regime. Dynamic mode decomposition analysis revealed that odd-order modes contribute to lift forces, while even-order modes result in drag forces. The flow structures are dominated by a small number of modes, and the energy of high-order modes increases with increasing amplitude. Different wake characteristics were observed for various gaps and amplitudes, which are related to the local pressure shapes on the cylinders.