Barkley D. & Henderson R. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.
Bender C. M. & Orszag S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
Bers A. 1975 Linear waves and instabilities. In Physique des Plasmas (ed. DeWitt C. & Peyraud J.), pp. 113–215. Gordon & Breach.
Blackburn H. M. & Henderson R. D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255–286.
Briggs R. 1964 Electron-Stream Interaction with Plasmas. MIT Press.
Chomaz J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 156, 209–240.
Chomaz J.-M., Huerre P. & Redekopp L. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths. 84, 119–144.
Cooper A. J. & Crighton D. G. 2000 Global modes and superdirective acoustic radiation in low-speed axisymmetrics jets. Eur. J. Mech. B/Fluids. 19, 559–574.
Coutanceau M. & Bouard R. 1977 Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. J. Fluid Mech. 79, 231–256.
Dennis S. R. C. & Chang G. 1970 Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100. J. Fluid Mech. 42, 471–489.
Drazin P. G. & Reid W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Dusěk J., Le Gal, P. & Fraunié P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 59–80.
Fadlun E. A., Verzicco R., Orlandi P. & Mohd-Yusof J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60.
Fornberg B. 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819–855.
Golub G. H. & Van Loan, C. 1989 Matrix Computations, 2nd edn. Johns Hopkins University Press.
Goujon-Durand S., Jenffer P. & Wesfreid J. E. 1994 Downstream evolution of the Bénard–von Kármán instability. Phys. Rev. Lett. 50, 308–313.
Hill D. C. 1992 A theoretical approach for analyzing the re-stabilization of wakes. AIAA Paper 92-0067.
Hinch E. J. 1994 Perturbation Methods. Cambridge University Press.
Huerre P. & Monkewitz P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.
Huerre P. & Monkewitz P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.
Ince E. L. 1926 Ordinary Differential Equations. Dover.
Jackson C. P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23–45.
Karniadakis G. E. & Triantafyllou G. S. 1992 Three-dimensional dynamics and transition to turbulence in the wakes of bluff bodies. J. Fluid Mech. 238, 1–30.
Kim J., Kim D. & Choi H. 2001 An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132–150.
Le Dizès, S., Huerre P., Chomaz J.-M. & Monkewitz P. A. 1996 Linear global modes in spatially developing media. Phil. Trans. R. Soc. Lond. 354, 169–212.
Mathis C., Provansal M. & Boyer L. 1984 Bénard–von Kármán instability: an experimental study near the threshold. J. Phys. Lett. Paris. 45, 483–491.
Mittal R. & Balachandar S. 1996 Direct numerical simulation of flow past elliptic cylinders. J. Comput. Phys. 124, 351–367.
Mohd-Yusof J. 1997 Combined immersed-boundary/B-spline methods for simulations of flows in complex geometries. Annu. Res. Briefs. Center for Turbulence Research, NASA Ames and Standford University, p. 317.
Monkewitz P. A., Huerre P. & Chomaz J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.
Morse P. M. & Feshbach H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Noack B. R. & Eckelmann H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297–330.
Pier B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.
Provansal M., Mathis C. & Boyer L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.
Schmid P. J. & Henningson D. S. 2001 Stability and Transition in Shear Flows. Springer.
Sheard G., Thompson M. & Hourigan K. 2001 A numerical study of bluff ring wake stability. In Proc. 14th Australasian Fluid Mech. Conf. Dep. Mech. Engng, University of Adelaide.
Sreenivasan K. R., Strykowski P. J. & Olinger D. J. 1987 Hopf bifurcation, Landau equation, and vortex shedding behind circular cylinders. In Proc. Forum on Unsteady Flow Separation (ed. Ghia K.), pp. 1–13. ASME.
Strykowski P. J. & Sreenivasan K. R. 1990 On the formation and suppression of vortex ‘shedding’ at low Reynolds number. J. Fluid Mech. 218, 71–107.
Tannehill J. C., Anderson D. A. & Pletcher R. H. 1997 Computational Fluid Mechanics and Heat Transfer, 2nd edn. Taylor & Francis.
Trefethen L. N., Trefethen A. E., Reddy S. C. & Driscoll T. A. 1993 Hydrodynamics stability without eigenvalues. Science. 261, 578–584.
Triantafyllou G. S. & Karniadakis G. E. 1990 Computational reducibility of unsteady viscous flows. Phys. Fluids A 2, 653–656.
Williamson C. H. K. 1988 Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids. 31, 2742–2744.
Williamson C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.
Winters K. H., Cliffe K. A. & Jackson C. P. 1986 The Prediction of Instabilities Using Bifurcation Theory. Wiley.
Yang X. & Zebib A. 1988 Absolute and convective instability of a cylinder wake. Phys. Fluids. 1, 689–696.
Ye T., Mittal R., Udaykumar H. S. & Shyy W. 1999 An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156, 209–240.
Zebib A. 1987 Stability of viscous flow past a circular cylinder. J. Engng Maths. 21, 155–165.
Zielinska B. J. A., Goujon-Durand S., Dusek J. & Wesfreid J. E. 1997 Strongly nonlinear effect in unstable wakes. Phys. Rev. Lett. 79, 3893–3896.
Zielinska B. J. A. & Wesfreid J. E. 1995 On the spatial structure of global modes in wake flows. Phys. Fluids. 7, 1418–1424.