The onset of instability and bifurcations in the transitional wake of two tandem square cylinders

Abstract

Unsteady three-dimensional simulations are performed to elucidate the hidden transitional flow dynamics and Hopf bifurcations along the topological corelines of the created von Kármán streets behind a pair of square cylinders positioned in tandem. Our simulations provide significant new insight into the three-dimensional wake evolution and governing flow physics. We explain how pressure, velocity, and vorticity fluctuation along the Kármán vortex corelines in the increasingly unstable wake amplify, facilitating the growth of various modal instability patterns. The existing knowledge of wake transition through the intertwining of modes A, B, and C instabilities and associated linear stability analysis helped to gain some insight into the overall wake feature. The current study explains how exactly the transitional disturbances physically spread behind a pair of inline and tandem cylinders through the self-excited spanwise-periodic oscillation of the wake and created a sequence of variable length scaled Hopf bifurcations and their swapping for varied gaps between the cylinders and Reynolds number. The growth of a slow mode of the spectral frequency at the bifurcation points seemed crucial in initiating the near-transitional flow irregularity.