While the wake of a circular cylinder and, to a lesser extent, the normal flat plate have been studied in considerable detail, the wakes of elliptic cylinders have not received similar attention. However, the wakes from the first two bodies have considerably different characteristics, in terms of three-dimensional transition modes, and near- and far-wake structure. This paper focuses on elliptic cylinders, which span these two disparate cases. The Strouhal number and drag coefficient variations with Reynolds number are documented for the two-dimensional shedding regime. There are considerable differences from the standard circular cylinder curve. The different three-dimensional transition modes are also examined using Floquet stability analysis based on computed two-dimensional periodic base flows. As the cylinder aspect ratio (major to minor axis) is decreased, mode A is no longer unstable for aspect ratios below 0.25, as the wake deviates further from the standard Bénard–von Kármán state. For still smaller aspect ratios, another three-dimensional quasi-periodic mode becomes unstable, leading to a different transition scenario. Interestingly, for the 0.25 aspect ratio case, mode A restabilises above a Reynolds number of approximately 125, allowing the wake to return to a two-dimensional state, at least in the near wake. For the flat plate, three-dimensional simulations show that the shift in the Strouhal number from the two-dimensional value is gradual with Reynolds number, unlike the situation for the circular cylinder wake once mode A shedding develops. Dynamic mode decomposition is used to characterise the spatially evolving character of the wake as it undergoes transition from the primary Bénard–von Kármán-like near wake into a two-layered wake, through to a secondary Bénard–von Kármán-like wake further downstream, which in turn develops an even longer wavelength unsteadiness. It is also used to examine the differences in the two- and three-dimensional near-wake state, showing the increasing distortion of the two-dimensional rollers as the Reynolds number is increased.

Two-dimensional flow past a cylinder close to a free surface at a Reynolds number of 180 is numerically investigated. The wake behaviour for Froude numbers between 0.0 and 0.7 and for gap ratios between 0.1 and 5.0 is examined. For low Froude numbers, where the surface deformation is minimal, the simulations reveal that this problem shares many features in common with flow past a cylinder close to a no-slip wall. This suggests that the flow is largely governed by geometrical constraints in the low-Froude-number limit. At Froude numbers in excess of 0.3–0.4, surface deformation becomes substantial. This can be traced to increases in the local Froude number to unity or higher in the gap between the cylinder and the surface. In turn, this is associated with supercritical to subcritical transitions in the near wake resulting in localized free-surface sharpening and wave breaking. Since surface vorticity is directly related to surface curvature, such high surface deformation results in significant surface vorticity, which can diffuse and then convect into the main flow, altering the development of Strouhal vortices from the top shear layer, affecting wake skewness and suppressing the absolute instability. The variations of parameters such as Strouhal number and formation length are provided for Froude numbers spanning the critical range. At larger Froude numbers, good agreement is obtained with recently published experimental investigations. The previously seen metastable wake states are observed to occur for similar system parameters to the experiments despite the difference in Reynolds numbers by a factor of about 40. The wake state switching appears to be controlled by a feedback loop. Important elements of the feedback loop include the cyclic generation and suppression of the absolute instability of the wake, and the role of surface vorticity and vortices formed from the bottom shear layer in controlling vortex formation from the top shear layer. The proposed mechanism is presented. Shedding ceases at very small gap ratios (${\sim}\, 0.1$–0.2). This behaviour can be explained in terms of the fluid flux through the gap, vorticity diffusion into the surface and opposite-signed surface vorticity from the strong surface deformation.

The low-Reynolds-number wake dynamics and stability of the flow past toroids placed normal to the flow direction are studied numerically. This bluff body has the attractive feature of behaving like the sphere at small aspect ratios, and locally like the straight circular cylinder at large aspect ratios. Importantly, the geometry of the ring is described by a single parameter, the aspect ratio ($\hbox{\it Ar}$), defined as a ratio of the torus diameter to the cross-sectional diameter of the ring. A rich diversity of wake topologies and flow transitions can therefore be investigated by varying the aspect ratio. Studying this geometry allows our understanding to be developed as to why the wake transitions leading to turbulence for the sphere and circular cylinder differ so greatly. Strouhal–Reynolds-number profiles are determined for a range of ring aspect ratios, as are critical Reynolds numbers for the onset of flow separation, unsteady flow and asymmetry. Results are compared with experimental findings from the literature. Calculated Strouhal–Reynolds-number profiles show that ring wakes shed at frequencies progressively closer to that of the straight circular cylinder wake as aspect ratio is increased from $\hbox{\it Ar}\,{ =}\, 3$. For $\hbox{\it Ar} \,{>}\, 8$, the initial asymmetric transition is structurally analogous to the mode A transition for the circular cylinder, with a discontinuity present in the Strouhal–Reynolds-number profile. The present numerical study reveals a shedding-frequency decrease with decreasing aspect ratio for ring wakes, and an increase in the critical Reynolds numbers for flow separation and the unsteady flow transition. A Floquet stability analysis has revealed the existence of three modes of asymmetric vortex shedding in the wake of larger rings. Two of these modes are analogous to mode A and mode B of the circular cylinder wake, and the third mode, mode C, is analogous to the intermediate wavelength mode found in the wake of square section cylinders and circular cylinder wakes perturbed by a tripwire. Furthermore, three distinct asymmetric transition modes have been identified in the wake of small aspect ratio bluff rings. Fully developed asymmetric simulations have verified the unsteady transition for rings that exhibit a steady asymmetric wake.