Modal Analysis of Oscillating Laminar Flow Behind Tandem and Parallel Cylinders Using Dynamic Mode Decomposition

Flow past cylinders exhibits oscillatory behavior beyond a critical Reynolds number, with vortex shedding affecting the lift and drag coefficients. This study analyzes the wake dynamics of tandem and side-by-side cylinder configurations at Reynolds numbers 100 and 250 using Dynamic Mode Decomposition (DMD) and examines how the extracted wake modes relate to the resulting force coefficients. For the tandem configuration, the oscillation frequency of the lift coefficient is identified via a Fast Fourier Transform (FFT), and the corresponding wake is decomposed into DMD modes that characterize its spatial structure. The frequency of the dominant DMD mode matches the lift-coefficient oscillation frequency, establishing a clear connection between coherent wake structures and the unsteady forces on the cylinders. In the side-by-side configuration, the wake exhibits distinct behaviors at the two Reynolds numbers, reflecting different instability mechanisms. Across both configurations, a consistent link is found between the force coefficients and the wake modes. The flow is reconstructed using the dominant DMD modes, thus giving a reduced-order model of the wake dynamics. These findings provide a framework for understanding multi-cylinder wake dynamics by drawing connections between data-driven modal decomposition and classical spectral analysis techniques.