Abstract
Linear stability analysis of a wide range of twodimensional and axisymmetric bluffbody wakes shows that the first threedimensional mode to became unstable is always mode E. From the studies presented in this paper, it is speculated to be the universal primary 3D instability, irrespective of the flow configuration. However, since it is a transition from a steady twodimensional flow, whether this mode can be observed in practice does depend on the nature of the flow setup. For example, the mode E transition of a circular cylinder wake occurs at a Reynolds number of Re ≃96, which is considerably higher than the steady to unsteady Hopf bifurcation at Re ≃96 leading to BénardvonKármán shedding. On the other hand, if the absolute instability responsible for the latter transition is suppressed, by rotating the cylinder or moving it towards a wall, then mode E may become the first transition of the steady flow. A wellknown example is flow over a backwardfacing step, where this instability is the first global instability to be manifested on the otherwise twodimensional steady flow. Many other examples are considered in this paper. Exploring this further, a structural stability analysis (Pralits et al. J. Fluid Mech., vol. 730, 2013, pp. 518) was conducted for the subset of flows past a rotating cylinder as the rotation rate was varied. For the nonrotating or slowly rotating case, this indicated that the growth rate of the instability mode was sensitive to forcing between the recirculation lobes, while for the rapidly rotating case, it confirmed sensitivity near the cylinder and towards the hyperbolic point. For the nonrotating case, the perturbation, adjoint and structural stability fields, together with the wavelength selection, show some similarities with those of a Crow instability of a counterrotating vortex pair, at least within the recirculation zones. On the other hand, at much higher rotation rates, Pralits et al. (J. Fluid Mech., vol. 730, 2013, pp. 518) have suggested that hyperbolic instability may play a role. However, both instabilities lie on the same continuous solution branch in Reynolds number/rotationrate parameter space. The results suggest that this particular flow transition at least, and probably others, may have a number of different physical mechanisms supporting their development.
Original language  English 

Pages (fromto)  5066 
Number of pages  17 
Journal  Journal of Fluid Mechanics 
Volume  792 
DOIs  
Publication status  Published  10 Apr 2016 
Keywords
 Instability
 Parametric instability
 Wakes
Equipment

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