Spanwise bifurcations beneath the bluff-body instability modes

Abstract

A new family of bifurcations is detected in a cylinder wake. The simulations reveal the presence of physically significant spanwise wavy flow undulation in the near-wake of a square cylinder which plays an important role in the modal transition. The alternate process of vortex shedding initiates a systematic cross-stream momentum transfer that activates self-sustained spanwise oscillation of the physical wake, leading to the growth of sequence of Hopf bifurcations along the topological cores of von Kármán vortices. The study exhibits how exactly such self-excited spanwise oscillatory fluctuations of pressure, velocity, and KE keep growing along a vortex-core for increased Re and distinctly influence the growth of “Mode A” and “Mode B” instability. It reports existence of two distinct stages of wake undulation over 125 ≤ Re ≤ 240. While the weakly subcritical spanwise-periodic oscillations of pressure, velocity, vorticity, and associated uniform and wider length-scale bifurcations along the von Kármán vortex corelines dominate during “Mode A” instability, the transition to the “Mode B” is prompted following faster and random eruption (and swapping) of significantly smaller but variable length-scaled bifurcations and accompanied low frequency non-uniform fluctuation of flow variables. Such unstable flow perturbations and resulting bifurcations along the von Kármán vortex cores apparently influence generation of longitudinal vortical ribs (Mode A and Mode B) in the wake. The appearance of a slow varying secondary frequency at the bifurcation points seemed crucial for initiating the spanwise flow irregularity and transition to “Mode B.”