Mode A secondary instability in wake transition

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Abstract
It is now well known that the wake transition regime for a circular cylinder involves two modes of secondary three‐dimensional instability (modes ‘‘A’’ and ‘‘B’’), depending on the regime of Reynolds number (Re). However, there exists a surprisingly large scatter in previous measurements of critical Re for the inception of the mode A instability (Re from 140 to 190) and in previous measurements of spanwise length scale. It is deduced in this work that the large variation in previous measurements concerning mode A are due to the presence of vortex dislocations. In the absence of such dislocations, we find an excellent agreement of the critical Re as well as spanwise wavelength of mode A with the linear secondary stability analysis of Henderson and Barkley [Phys. Fluids 8, 1683 (1996)]. We further demonstrate that these large‐scale dislocations in wake transition are triggered at the sites of some of the vortex loops for mode A; they are an intrinsic feature of transition, independent of end conditions. These studies lead us to a new clarification of the possible flow states through wake transition, as follows. If one defines a Mode A* as (Mode A+Dislocations), then the route through transition appears to follow the scenario of wake modes: (2D→A→A*→B).