On axisymmetric bluff body wakes: three-dimensional wake structures and transition criticality of the torus

Three bluff ring aspect ratios are studied numerically to elucidate the various three-dimensional transition modes previously predicted in the wakes of bluff rings by linear stability analysis. The transitions are modeled with respect to the Landau equation, and the criticality of the various transitions is determined from the coefficients of the Landau equation. The wake flow fields are simulated using a spectral-element scheme, incorporating a Fourier expansion of the two-dimensional grids in the spanwise direction to evolve the three-dimensional wake flow. Linear Floquet stability analysis performed previously on the wakes of bluff rings has predicted numerous three-dimensional transitions at various aspect ratios. Bluff rings with smaller aspect ratios (those approaching the sphere geometry) are predicted to undergo a regular three-dimensional transition (ie. steady to steady flow), followed by a Hopf bifurcation to an unsteady wake with increasing Reynolds number. Three transition modes have been identified in this aspect ratio range, referred to as Modes I, II and III respective to increasing aspect ratio. Plots visualizing the aforementioned transition modes are provided, and the transitions are modeled with the Landau equation, allowing the criticality of the various modes to be determined. 1