Chaotic dynamics of two-dimensional flows around a cylinder

Abstract

We study flow around a cylinder from a dynamics perspective, using drag and lift as indicators. We observe that the mean drag coefficient bifurcates from the steady case when the Karman vortex street emerges. We use standard dynamics metrics to analyze the drag/lift phase diagram. We also find a jump in the dimension of the drag/lift attractor just above Reynolds number of 200, indicating a breakdown of periodicity. We compare the simulated drag values with experimental data obtained over the last hundred years. Although there is substantial agreement, we note a Reynolds number range where there is a substantial, unexplained discrepancy with data from over a hundred years ago. Our simulations suggest that a vibrational resonance in the cylinder would be unlikely for Reynolds numbers greater than 1000, where the drag/lift behavior is fully chaotic.