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



An exhaustive parametric study of the transition scenario in the wake of oblate spheroids and flat cylinders placed with their rotation axis parallel to the flow is presented. The flatness of the investigated objects is classified by the aspect ratio χ defined as χ = d/a for spheroids (with d the diameter and a the length of the polar axis) and as χ = d/h) for cylinders (with h the cylinder height). We find a significant qualitative similarity between both configurations. At large aspect ratios (χ > 2.3 for spheroids and χ ≥ 4 for cylinders), the secondary bifurcation giving rise to a periodic state without planar symmetry is subcritical with a hysteresis interval of about two Reynolds number units. For spheroids, the sphere-like scenario is recovered only at aspect ratios very close to one (χ ≥ 1 are considered), while for cylindrical bodies the same holds for χ ≤ 1.7. For intermediate aspect ratios, a domain of states with non-zero net helicity separates states typical for the sphere wake from those of an infinitely flat disk.


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Auguste, F., Fabre, D. & Magnaudet, J. 2010 Bifurcations in the wake of a thick circular disk. Theor. Comput. Fluid Dyn. 24, 305313.
Bouchet, G., Mebarek, M. & Dušek, J. 2006 Hydrodynamic forces acting on a rigid fixed sphere in early transitional regimes. Eur. J. Mech. B Fluids 25, 321336.
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20, 051702.
Fernandes, P. C., Risso, F., Ern, P. & Magnaudet, J. 2007 Oscillatory motion and wake instability of freely rising axisymmetric bodies. J. Fluid Mech. 573, 479502.
Field, S. B., Klaus, M. & Moore, M. G. 1997 Chaotic dynamics of falling disks. Nature 388, 252254.
Ghidersa, B. & Dušek, J. 2000 Breaking of axisymetry and onset of unsteadiness in the wake of a sphere. J. Fluid Mech. 423, 3369.
Jenny, M. & Dušek, J. 2004 Efficient numerical method for the direct numerical simulation of the flow past a single light moving spherical body in transitional regimes. J. Comput. Phys. 194, 215232.
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 1970.
Kotouč, M., Bouchet, G. & Dušek, J. 2009 a Drag and flow reversal in mixed convection past a heated sphere. Phys. Fluids 21, 054104.
Kotouč, M., Bouchet, G. & Dušek, J. 2009 b Transition to turbulence in the wake of a fixed sphere in mixed convection. J. Fluid Mech. 625, 205248.
Meliga, P., Chomaz, J. M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion. J. Fluid Mech. 633, 159189.
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323344.
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds number. J. Fluid Mech. 605, 253262.
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos. Addison-Wesley.
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Parametric study of the transition in the wake of oblate spheroids and flat cylinders



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