Parametric study of the transition in the wake of oblate spheroids and flat cylinders

Recently, the wake of a flat disk has regained the interest of researchers.\footnote{Fabre, Auguste and Magnaudet Physics of Fluids 20, 051702 (2008); Meliga, Chomaz and Sipp, J. Fluid Mech. 633, 159 (2009)} Simultaneously, some numerical simulations were concerned with cylindrical bodies of finite thickness and showed\footnote{Auguste, Fabre and Magnaudet, Theor. Comput. Fluid Dyn. 24, 305 (2010)} that the wakes of such bodies present a different scenario from that of a flat disk and that of a sphere (which is widely known and accepted\footnote{Bouchet, Mebarek and Du\v{s}ek, Eur. J. Mech. B/Fluids 25, 321 (2006)}). A systematic study covering the whole range of cylinders of aspect ratio (diameter/thickness) between one and infinity as well as a study concerning oblate spheroids which establishes the link between the wake of a sphere and that of an infinitely flat disk, which until now was missing, will be the topic of this communication. The state diagram obtained for oblate spheroids illustrating the transition between the scenario of a sphere wake and that of a flat disk will be presented and discussed.