Steady flow past a torus with aspect ratio less than 5

Steady flow past a torus with an aspect ratio less than 5 and its axis aligned with the flow is studied numerically by solving the steady, axisymmetric Navier–Stokes equations. The wake structure behind tori exhibits diverse behaviours. The detached recirculating zone on the axis, the attached recirculating zone, and the detached recirculating zone behind the torus tube may appear individually or concurrently, depending on the aspect ratio and the Reynolds number. A wake structure map is summarized based on the observed flow behaviours. Six flow regimes with different wake behaviours are identified and the corresponding flow regime map is plotted, which include the no-recirculating-zone regime, the single-detached-recirculating-zone regime, the single-attached-recirculating-zone regime, the two-recirculating-zone regime I, the two-recirculating-zone regime II, and the three-recirculating-zone regime. Over the range of aspect ratio 1.9