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Low-dimensional dynamics of a turbulent axisymmetric wake

  • G. Rigas (a1), A. R. Oxlade (a1), A. S. Morgans (a1) and J. F. Morrison (a1)


The coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter-based Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sim }2\times 10^5$ . Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and are manifested as unsteady vortex shedding with azimuthal wavenumber $m={\pm }1$ . In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of the symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the time scales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.


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Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209221.
Berger, E., Scholz, D. & Schumm, M. 1990 Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations. J. Fluids Struct. 4, 231257.
Bohorquez, P., Sanmiguel-Rojas, E., Sevilla, A., Jiménez-González, J. I. & Martínez-Bazán, C. 2011 Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body. J. Fluid Mech. 676, 110144.
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351386.
Bury, Y. & Jardin, T. 2012 Transitions to chaos in the wake of an axisymmetric bluff body. Phys. Lett. A 376, 32193222.
Frisch, U. 1996 Turbulence. Cambridge University Press.
Fuchs, H. V., Mercker, E. & Michel, U. 1979 Large-scale coherent structures in the wake of axisymmetric bodies. J. Fluid Mech. 93, 185207.
Grandemange, M.2013 Analysis and control of three-dimensional turbulent wakes: from axisymmetric bodies to real road vehicles. PhD thesis, ENSTA ParisTech.
Grandemange, M., Gohlke, M. & Cadot, O. 2013 Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability. J. Fluid Mech. 722, 5184.
Grandemange, M., Gohlke, M., Parezanović, V. & Cadot, O. 2012 On experimental sensitivity analysis of the turbulent wake from an axisymmetric blunt trailing edge. Phys. Fluids 24, 035106.
Holmes, P., Lumley, J. L., Berkooz, G. & Rowley, C. W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd edn. Cambridge University Press.
Hucho, W.-H.(Ed.) 1998 Aerodynamics of Road Vehicles, 4th edn. Society of Automotive Engineers, SAE.
Lin, N., Reed, H. L. & Saric, W. S. 1992 Effect of leading-edge geometry on boundary-layer receptivity to freestream sound. In Instability, Transition, and Turbulence, pp. 421440. Springer.
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic Press.
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.
Oxlade, A. R.2013 High-frequency periodic jet forcing of a turbulent axisymmetric wake. PhD thesis, Imperial College.
Pier, B. 2008 Local and global instabilities in the wake of a sphere. J. Fluid Mech. 603, 3962.
Qubain, A.2009 Active control of a turbulent bluff body wake. PhD thesis, Imperial College.
Sanmiguel-Rojas, E., Sevilla, A., Martínez-Bazán, C. & Chomaz, J.-M. 2009 Global mode analysis of axisymmetric bluff-body wakes: stabilization by base bleed. Phys. Fluids 21, 114102.
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, 34603469.
Taneda, S. 1978 Visual observations of the flow past a sphere at Reynolds numbers between $10^4$ and $10^6$ . J. Fluid Mech. 85, 187192.
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 4573.
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Low-dimensional dynamics of a turbulent axisymmetric wake

  • G. Rigas (a1), A. R. Oxlade (a1), A. S. Morgans (a1) and J. F. Morrison (a1)


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