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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.

A recent numerical study by Rao et al. (J. Fluid Mech., vol. 717, 2013, pp. 1–29) predicted the existence of several previously unobserved linearly unstable three-dimensional modes in the wake of a spinning cylinder in cross-flow. While linear stability analysis suggests that some of these modes exist for relatively limited ranges of Reynolds numbers and rotation rates, this may not be true for fully developed nonlinear wakes. In the current paper, we present the results of water channel experiments on a rotating cylinder in cross-flow, for Reynolds numbers $200\leqslant \mathit{Re}\leqslant 275$ and non-dimensional rotation rates $0\leqslant \alpha \leqslant 2. 5$. Using particle image velocimetry and digitally post-processed hydrogen bubble flow visualizations, we confirm the existence of the predicted modes for the first time experimentally. For instance, for $\mathit{Re}= 275$ and a rotation rate of $\alpha = 1. 7$, we observe a subharmonic mode, mode C, with a spanwise wavelength of ${\lambda }_{z} / d\approx 1. 1$. On increasing the rotation rate, two modes with a wavelength of ${\lambda }_{z} / d\approx 2$ become unstable in rapid succession, termed modes D and E. Mode D grows on a shedding wake, whereas mode E consists of streamwise vortices on an otherwise steady wake. For $\alpha \gt 2. 2$, a short-wavelength mode F appears localized close to the cylinder surface with ${\lambda }_{z} / d\approx 0. 5$, which is presumably a manifestation of centrifugal instability. Unlike the other modes, mode F is a travelling wave with a spanwise frequency of ${\mathit{St}}_{3D} \approx 0. 1$. In addition to these new modes, observations on the one-sided shedding process, known as the ‘second shedding’, are reported for $\alpha = 5. 1$. Despite suggestions from the literature, this process seems to be intrinsically three-dimensional. In summary, our experiments confirm the linear predictions by Rao et al., with very good agreement of wavelengths, symmetries and the phase velocity for the travelling mode. Apart from this, these experiments examine the nonlinear saturated state of these modes and explore how the existence of multiple unstable modes can affect the selected final state. Finally, our results establish that several distinct three-dimensional instabilities exist in a relatively confined area on the $\mathit{Re}$–$\alpha $ parameter map, which could account for their non-detection previously.

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The variation of Strouhal number with Reynolds number is quantified experimentally for a series of elliptical cylinders spanning aspect ratios between \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ar}}=1$\end{document}Ar=1, corresponding to a circular cylinder, and \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ar}}=0$\end{document}Ar=0, corresponding to a flat plate, over the Reynolds number range \documentclass[12pt]{minimal}\begin{document}$100 \leqslant \mbox{\textit {Re}}\leqslant 300$\end{document}100⩽Re⩽300. The widths of the spectral peaks in Fourier space at each Reynolds number, together with changes in the shape or continuity of the Strouhal number curves, provide information of underlying three-dimensional transitions. Whilst modified versions of the mode A and B transitions of a circular cylinder wake occur at aspect ratios above \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ar}}\approx 0.4$\end{document}Ar≈0.4, one major difference is observed for \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ar}}\lesssim 0.4$\end{document}Ar≲0.4. In a limited range of Reynolds numbers, the wake appears to re-laminarize after it has already undergone three-dimensional transition. This flow regime is characterized by a strictly periodic vortex shedding.