On Dynamic Mode Decomposition: Application on Flow Past an Oscillatory Cylinder

The capacity of Dynamic Mode Decomposition (DMD) as a data-inspired methodology to discern spatial-temporal structures and predict future states in intricate dynamical systems is the focal point of this investigation. This methodology is employed on a system comprising a flow past a cylinder at a Reynolds number of 250 and a Strouhal number of 2.5. The study aims at utilizing DMD to deconstruct the underpinning flow dynamics, detect coherent structures associated with spatial modes, and assess its predictive capacity. The investigation pivots around three unique scenarios, each highlighting a different boundary condition for the cylinder. These include the flow dynamics past a stationary cylinder, perpetually anti-clockwise rotating cylinder, and an oscillatory rotating cylinder, with the oscillation frequency equal to the vortex shedding frequency of the first case. The examination of these cases allows for an evaluation of DMD's prowess in capturing the modes relevant to each flow condition and its potential for future state prediction. The implementation of DMD allows for the effective detection of the dominant modes pertinent to the diverse flow conditions. This facilitates a comprehensive understanding of the spatiotemporal characteristics of the flow past the cylinder. The temporal analysis of modes in each case identifies the energy flow and capturing of dominant frequencies among different modes, indicating system harmonics. This phenomenon is specific to Hopf bifurcation, which is the characteristic of a periodic flows at Re > 47. Using the identified modes, the temporal evolution of the flow is extrapolated, enabling accurate predictions that extend beyond the available data. This aspect is especially significant in areas like flow control and optimization, where accurate future state prediction is vital.