Asymmetric structure and non-linear transition behaviour of the wakes of toroidal bodies

Abstract

The flow past three different aspect ratio toroids is studied numerically to elucidate the various non-axisymmetric wake transition modes previously predicted by linear stability analysis. The transitions are modelled 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 azimuthal direction to evolve the three-dimensional wake flow. Linear Floquet stability analysis performed previously on the wakes of bluff rings has predicted a series of non-axisymmetric transitions at various aspect ratios. Bluff rings with smaller aspect ratios (those approaching the sphere geometry) are predicted to undergo a regular asymmetric transition (i.e., 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. Tracer particle and iso-surface plots visualizing the aforementioned transition modes are provided, which reveal the details of the wake structure associated with the saturated modes.