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Local and global instabilities in the wake of a sphere

Published online by Cambridge University Press:  30 April 2008

BENOÎT PIER
BENOÎT PIER*
Affiliation:
Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon, CNRS, Université Claude-Bernard Lyon 1, INSA Lyon, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France
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Abstract

The global dynamics of open shear flows is closely related to the nature of their local instability characteristics, either convective or absolute. The present investigation revisits the wake of a sphere, obtains its global behaviour by direct numerical simulations and derives its local stability features, computed for the underlying basic flow under a quasi-parallel flow assumption. It is shown that both the axisymmetric and the planar symmetric basic flows exhibit domains of local absolute instability in the near-wake region. The largest absolute growth rates occur for instabilities developing on the non-axisymmetric basic wake and conserving its planar symmetry.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 603 , 25 May 2008 , pp. 39 - 61
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Maxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 068102.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750–756.CrossRefGoogle Scholar
Bers, A. 1983 Space-time evolution of plasma instabilities—absolute and convective. In Handbook of plasma physics (ed. Rosenbluth, M. & Sagdeev, R.), pp. 451–517. North–Holland.Google Scholar
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, 321–336.CrossRefGoogle Scholar
Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods. Dover.Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. J. & Quarteroni, A. 1988 Spectral Methods in Fluid Dynamics. Springer.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Gallaire, F., Ruith, M., Meiburg, E., Chomaz, J.-M. & Huerre, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 71–80.CrossRefGoogle Scholar
Ghidersa, B. & Duček, J. 2000 Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere. J. Fluid Mech. 423, 33–69.CrossRefGoogle Scholar
Goda, K. 1979 A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. J. Comut. Phys. 30, 76–95.CrossRefGoogle Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 159–229. Cambridge: University Press.Google Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.CrossRefGoogle Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393–409.CrossRefGoogle Scholar
Mittal, R. 1999 Planar symmetry in the unsteady wake of a sphere. AIAA J. 37, 388–390.CrossRefGoogle Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.CrossRefGoogle Scholar
Monkewitz, P. A. 1988 a The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids 31, 999–1006.CrossRefGoogle Scholar
Monkewitz, P. A. 1988 b A note on vortex shedding from axisymmetric bluff bodies. J. Fluid Mech. 192, 561–575.CrossRefGoogle Scholar
Nakamura, I. 1976 Steady wake behind a sphere. Phys. Fluids 19, 5–8.CrossRefGoogle Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344.CrossRefGoogle Scholar
Nichols, J. W., Schmid, P. J. & Riley, J. J. 2007 Self-sustained oscillations in variable-density round jets. J. Fluid Mech. 582, 341–376.CrossRefGoogle Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 Nonlinear synchronization in open flows. J. Fluids Struct. 15, 471–480.CrossRefGoogle Scholar
Pier, B., Huerre, P. & Chomaz, J.-M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 49–96.Google Scholar
Pier, B., Huerre, P., Chomaz, J.-M. & Couairon, A. 1998 Steep nonlinear global modes in spatially developing media. Phys. Fluids 10, 2433–2435.CrossRefGoogle Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.CrossRefGoogle Scholar
Raspo, I., Hugues, S., Serre, E., Randriamampianina, A. & Bontoux, P. 2002 A spectral projection method for the simulation of complex three-dimensional rotating flows. Computers Fluids 31, 745–767.CrossRefGoogle Scholar
Roos, F. W. & Willmarth, W. W. 1971 Some experimental results on sphere and disk drag. AIAA J. 9, 285–291.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1995 The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J. Fluid Mech. 287, 151–171.CrossRefGoogle Scholar
Schouveiler, L. & Provansal, M. 2002 Self-sustained oscillations in the wake of a sphere. Phys. Fluids 14, 3846–3854.CrossRefGoogle Scholar
Sevilla, A. & Martínez-Bazán, C. 2004 Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: local linear instability and global bleed control. Phys. Fluids 16, 3460–3469.CrossRefGoogle Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar