Low reynolds number flow around tori of different slenderness

We present the results of axisymmetric and three-dimensional numerical simulations of the flow around a torus in the low Reynolds number regime [10-2; 3 × 103] and aspect-ratio 0 < Gcyrillic = 2a/R ≤ 2 (core diameter over toroidal radius). It is shown that as Gcyrillic → 0, consistent with intuition and the results from the literature, the flow tends to that of a two-dimensional circular cylinder while for G → 2 the flow is that around a bluff obstacle. It has been observed that in a small region of the Re-Gcyrillic phase space, the flow develops an axisymmetric recirculation detached from the torus and with a vorticity distribution that resembles the Hill vortex. In the range 0 < Gcyrillic ≤ 2, several different regimes have been observed; the peculiarities of each regime are analyzed and, whenever possible, similarities and differences with other classical flows are discussed.