From the circular cylinder to the flat plate wake: The variation of Strouhal number with Reynolds number for elliptical cylinders

Abstract

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.