G. Ahlers and D. S. Cannell, Vortex-Front Propagation in Rotating Couette-Taylor Flow, Physical Review Letters, vol.50, issue.20, pp.1583-1586, 1983.
DOI : 10.1103/PhysRevLett.50.1583

A. Akonur and R. M. Lueptow, Three-dimensional velocity field for nonwavy and wavy Taylor Couette flow, J. Fluid Mech, 2001.
DOI : 10.1063/1.1556615

M. E. Ali and P. D. Weidman, On the linear stability of cellular spiral Couette flow, Physics of Fluids A: Fluid Dynamics, vol.5, issue.5, pp.1188-1200, 1993.
DOI : 10.1063/1.858604

T. , A. De-roquefort, and A. G. Grillaud, Computation of Taylor vortex flow by a transient implicit method, Computers & Fluids, vol.6, pp.259-269, 1978.

C. David-andereck, R. Dickman, and H. L. Swinney, New flows in a circular Couette system with co-rotating cylinders, Physics of Fluids, vol.26, issue.6, pp.1395-1401, 1983.
DOI : 10.1063/1.864328

C. David-andereck, S. S. Liu, and H. L. Swinney, Flow regimes in a circular Couette system with independently rotating cylinders, Journal of Fluid Mechanics, vol.16, issue.-1, pp.155-183, 1986.
DOI : 10.1017/S0022112084000021__S0022112084000021

J. Antonijoan, F. J. Marques, and . Sanchez, Non-linear spirals in the Taylor???Couette problem, Physics of Fluids, vol.10, issue.4, pp.3147-3159, 1998.
DOI : 10.1063/1.869606

J. J. Antonijoan and . Sanchez, Transitions from Taylor vortex flow in a co-rotating Taylor???Couette system, Physics of Fluids, vol.12, issue.12, pp.3147-3159, 2000.
DOI : 10.1063/1.1313385

G. K. Batchelor, NOTE ON A CLASS OF SOLUTIONS OF THE NAVIER-STOKES EQUATIONS REPRESENTING STEADY ROTATIONALLY-SYMMETRIC FLOW, The Quarterly Journal of Mechanics and Applied Mathematics, vol.4, issue.1, pp.29-41, 1951.
DOI : 10.1093/qjmam/4.1.29

T. B. Benjamin, Bifurcation Phenomena in Steady Flows of a Viscous Fluid. I. Theory, Proc. R. Soc. Lond. A, pp.1-26, 1978.
DOI : 10.1098/rspa.1978.0028

T. B. Benjamin, Bifurcation Phenomena in Steady Flows of a Viscous Fluid. II. Experiments, Proc. R. Soc. Lond. A, pp.27-43, 1978.
DOI : 10.1098/rspa.1978.0030

T. B. Benjamin and T. Mullin, Anomalous Modes in the Taylor Experiment, Proc. Roy. Soc. Lond. A, pp.221-249, 1981.
DOI : 10.1098/rspa.1981.0122

T. Berland, T. J. Jøssang, and . Feder, An Experimental Study of the Connection Between the Hydrodynamic and Phase-Transition Descriptions of the Couette-Taylor Instability, Physica Scripta, vol.34, issue.5, pp.427-431, 1986.
DOI : 10.1088/0031-8949/34/5/012

J. E. Burkhalter and E. L. Koschmieder, Steady supercritical Taylor vortex flow, Journal of Fluid Mechanics, vol.21, issue.03, pp.547-560, 1973.
DOI : 10.1146/annurev.fl.03.010171.002023

J. E. Burkhalter and E. L. Koschmieder, Steady supercritical Taylor vortices after sudden starts, Physics of Fluids, vol.17, issue.11, pp.17-1929, 1974.
DOI : 10.1063/1.1694646

A. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

P. Chossat-and-g and . Iooss, The Taylor-Couette Problem, 1994.
DOI : 10.1007/978-1-4612-4300-7

K. A. Cliffe, J. J. Kobine, and T. Mullin, The Role of Anomalours Modes in Taylor-Couette Flow, Proc. R. Soc. London A, pp.341-357, 1992.

K. A. Cliffe-and-t and . Mullin, A numerical and experimental study of anomalous modes in the Taylor experiment, Journal of Fluid Mechanics, vol.135, issue.-1, pp.243-258, 1985.
DOI : 10.1002/fld.1650020103

J. A. Cole, Taylor-vortex instability and annulus-length effects, Journal of Fluid Mechanics, vol.96, issue.01, pp.1-15, 1976.
DOI : 10.1017/S0022112076000098

P. W. Colovas and C. D. Andereck, Turbulent bursting and spatiotemporal intermittencyin the counterrotating Taylor-Couette system, Physical Review E, vol.55, issue.3, pp.2736-2741, 1997.
DOI : 10.1103/PhysRevE.55.2736

K. T. Coughlin and P. S. Marcus, Modulated waves in Taylor-Couette flow

K. T. Coughlin and P. S. Marcus, Modulated waves in Taylor-Couette flow Part 2. Numerical simulation, Journal of Fluid Mechanics, vol.5, issue.-1, pp.19-46, 1992.
DOI : 10.1017/S0022112084000896

R. C. Di-prima, P. M. Eagles-and-b, and . Ng, The effect of radius ratio on the stability of Couette flow and Taylor vortex flow, Physics of Fluids, vol.27, issue.10, pp.2403-2411, 1984.
DOI : 10.1063/1.864544

R. C. Di and H. L. Swinney, Instabilities and Transitions in Flow Between Concentric Rotating Cylinders. ²Topics in Applied Physics : Hydrodynamic Instabilities and the Transition to Turbulence, pp.139-180, 1981.

R. J. Donnelly, Taylor???Couette Flow: The Early Days, Physics Today, vol.44, issue.11, pp.32-39, 1991.
DOI : 10.1063/1.881296

W. S. Edwards, R. P. Tagg, B. C. Dornblaser, and H. L. Swinney, Periodic travelling waves with nonperiodic pressure, Eur. J. Mech., B/Fluids, vol.10, issue.2, pp.205-210, 1991.

V. W. Ekman, On the influence of the Earth's rotation on the ocean currents, Ark. Mat. Astr. Fys, vol.2, issue.11, pp.1-52, 1905.

P. R. Fenstermacher, H. L. Swinney, and J. P. Gollub, Dynamical instabilities and the transition to chaotic Taylor vortex flow, Journal of Fluid Mechanics, vol.31, issue.01, pp.103-128, 1979.
DOI : 10.1063/1.1691991

S. S. Ghosh-moulic-and-l and . Yao, Taylor-Couette instability of travelling waves with a continuous spectrum, J. Fluid Mech, vol.324, pp.181-198, 1996.

A. Goharzadeh-and-i and . Mutabazi, Experimental characterization of intermittency regimesin the Couette-Taylor system, The European Physical Journal B, vol.19, issue.1, pp.157-162, 2001.
DOI : 10.1007/s100510170360

J. P. Gollub and M. H. Freilich, Optical heterodyne test of perturbation expansions for the Taylor instability, Physics of Fluids, vol.19, issue.5, pp.618-626, 1976.
DOI : 10.1063/1.861520

M. Golubitsky and W. F. Langford, Pattern formation and bistability in flow between counterrotating cylinders, Physica D: Nonlinear Phenomena, vol.32, issue.3, pp.362-392, 1988.
DOI : 10.1016/0167-2789(88)90063-2

H. P. Greenspan, The theory of rotating fluids, Cambridge Monographs on Mechanics and Applied Mathematics, 1969.

J. J. Hegseth, C. David-andereck, F. Hayot, and Y. Pomeau, Spiral Turbulence and Phase Dynamics, Physical Review Letters, vol.62, issue.3, pp.257-260, 1989.
DOI : 10.1103/PhysRevLett.62.257

J. J. Hegseth, G. W. Baxter, and C. D. Andereck, Bifurcations from Taylor vortices between corotating concentric cylinders, Physical Review E, vol.53, issue.1, pp.507-521, 1996.
DOI : 10.1103/PhysRevE.53.507

R. M. Heinrichs, D. S. Cannell, G. Ahlers, and M. Jefferson, Experimental test of the perturbation expansion for the Taylor instability at various wavenumbers, Physics of Fluids, vol.31, issue.2, pp.250-255, 1988.
DOI : 10.1063/1.866855

S. A. Hugues and . Randriamampianina, An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, vol.15, issue.3, pp.501-521, 1998.
DOI : 10.1002/(SICI)1097-0363(19980915)28:3<501::AID-FLD730>3.0.CO;2-S

C. A. Jones, On flow between counter-rotating cylinders, Journal of Fluid Mechanics, vol.258, issue.-1, pp.433-450, 1982.
DOI : 10.1086/147538

T. Von and . Karman, Über laminare und turbulente Reibung, Z. angew. Math. Mech, vol.1, pp.233-252, 1921.

G. P. King, Y. Li, W. Lee, H. L. Swinney, and P. S. Marcus, Wave speeds in wavy Taylor-vortex flow, Journal of Fluid Mechanics, vol.102, issue.-1, pp.365-390, 1984.
DOI : 10.1103/PhysRevLett.46.992

J. K. Koga and E. L. Koschmieder, Taylor vortices in short fluid columns, Physics of Fluids A: Fluid Dynamics, vol.1, issue.9, pp.1475-1478, 1989.
DOI : 10.1063/1.857325

D. Kuo and K. S. Ball, Taylor???Couette flow with buoyancy: Onset of spiral flow, Physics of Fluids, vol.9, issue.10, pp.2872-2884, 1997.
DOI : 10.1063/1.869400

R. J. Lingwood, Absolute instability of the Ekman layer and related rotating flows, Journal of Fluid Mechanics, vol.331, pp.405-428, 1997.
DOI : 10.1017/S0022112096004144

M. Lücke, M. Mihelcic-and-k, and . Wingerath, Front propagation and pattern formation of Taylor vortices growing into unstable circular Couette flow, Physical Review A, vol.31, issue.1, pp.31-396, 1985.
DOI : 10.1103/PhysRevA.31.396

P. S. Marcus, Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave, Journal of Fluid Mechanics, vol.52, issue.-1, pp.65-113, 1984.
DOI : 10.1103/PhysRevLett.48.1172

R. Meyer-spasche, Pattern formation in viscous flows : the Taylor-Couette problem and Rayleigh-Bénard convection, International Series of Numerical Mathematics, vol.128, 1999.
DOI : 10.1007/978-3-0348-8709-0

T. Mullin, Finite-Dimensional Dynamics in Taylor-Couette Flow, IMA Journal of Applied Mathematics, vol.46, issue.1-2, pp.109-119, 1991.
DOI : 10.1093/imamat/46.1-2.109

T. Mullin and T. B. Benjamin, Transition to oscillatory motion in the Taylor experiment, Nature, vol.19, issue.5791, pp.567-569, 1980.
DOI : 10.1038/288567a0

T. Mullin and C. Blohm, Bifurcation phenomena in a Taylor???Couette flow with asymmetric boundary conditions, Physics of Fluids, vol.13, issue.1, pp.136-140, 2001.
DOI : 10.1063/1.1329906

G. P. Neitzel, Numerical computation of time-dependent Taylor-vortex flows in finite-length geometries, Journal of Fluid Mechanics, vol.283, issue.-1, pp.51-66, 1984.
DOI : 10.1017/S002211207300008X

J. M. Owen and R. H. Rogers, Flow and Heat Transfert in Rotating-Disc Systems : rotating cavities. Mechanical engineering research studies, engineering design series, 1995.

G. Pfister-and-i and . Rehberg, Space-dependent order parameter in circular couette flow transitions, Physics Letters A, vol.83, issue.1, pp.19-22, 1981.
DOI : 10.1016/0375-9601(81)90537-5

G. Pfister, H. Schmidt, K. A. Cliffe-and-t, and . Mullin, Bifurcation phenomena in Taylor-Couette flow in a very short annulus, Journal of Fluid Mechanics, vol.384, issue.-1, pp.1-18, 1988.
DOI : 10.1017/S0022112082001876

A. Prigent, La spirale turbulente : motif de grande longueur d'onde dans les écoulements cisaillés turbulents, Thèse, 2001.

A. Prigent-and-o and . Dauchot, Visualization of a Taylor???Couette flow avoiding parasitic reflections, Physics of Fluids, vol.12, issue.10, pp.2688-2690, 2000.
DOI : 10.1063/1.1287654

I. Raspo, S. Hugues, E. Serre, A. R. , and P. Bontoux, A spectral projection method for the simulation of complex threedimensional rotating flows, Computers & Fluids, pp.31-745, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00833836

A. Recktenwald, M. Lücke, and H. M. Müller, Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis, Physical Review E, vol.48, issue.6, pp.4444-4454, 1993.
DOI : 10.1103/PhysRevE.48.4444

J. Sanchez, D. Crespo-and-r, and . Marques, Spiral Vortices Between Concentric Cylinders
DOI : 10.1007/978-94-011-1689-3_10

W. Schröder and H. B. Keller, Wavy Taylor-vortex flows via multigrid-continuation methods, Journal of Computational Physics, vol.91, issue.1, pp.197-227, 1990.
DOI : 10.1016/0021-9991(90)90011-O

E. Serre, Instabilités de couche limite dans les écoulements confinés en rotation Simulation numérique directe par une méthode spectrale de comportements complexes, Thèse, 2000.

E. Serre, E. Crespo, D. Arco, and P. Bontoux, Annular and spiral patterns in flows between rotating and stationary discs, Journal of Fluid Mechanics, vol.434, pp.65-100, 2001.
DOI : 10.1017/S0022112001003494

URL : https://hal.archives-ouvertes.fr/hal-00834951

E. Serre, M. Schaefer, and P. Bontoux, Vortex breakdown in a cylinder with a free surface, Computational Fluid and Solid Mechanics, pp.1125-1127, 2003.
DOI : 10.1016/B978-008044046-0.50275-X

URL : https://hal.archives-ouvertes.fr/hal-00834166

H. A. Snyder, Stability of Rotating Couette Flow. II. Comparison with Numerical Results, Physics of Fluids, vol.11, issue.8, pp.11-1599, 1968.
DOI : 10.1063/1.1692167

H. A. Snyder, Waveforms in rotating Couette flow, International Journal of Non-Linear Mechanics, vol.5, issue.4, pp.659-685, 1970.
DOI : 10.1016/0020-7462(70)90055-7

H. A. Snyder, Wave-number selection at finite amplitude in rotating Couette flow, Journal of Fluid Mechanics, vol.14, issue.02, pp.273-298, 1969.
DOI : 10.1063/1.1691991

H. A. Snyder and R. B. Lambert, Harmonic generation in Taylor vortices between rotating cylinders, Journal of Fluid Mechanics, vol.36, issue.03, pp.545-562, 1966.
DOI : 10.1016/0031-9163(64)90058-7

V. Sobolík, B. Izrar, F. Lusseyran, and S. Skali, Interaction between the Ekman layer and the Couette???Taylor instability, International Journal of Heat and Mass Transfer, vol.43, issue.24, pp.43-4381, 2002.
DOI : 10.1016/S0017-9310(00)00067-3

A. Spohn, M. Mory, and E. J. Hopfinger, Observations of vortex breakdown in an open cylindrical container with a rotating bottom, Experiments in Fluids, vol.14, issue.1-2, pp.70-77, 1993.
DOI : 10.1007/BF00196990

C. Stern-and-f and . Hussain, Chaos in counter-rotating Couette flow, Physica D: Nonlinear Phenomena, vol.72, issue.3, pp.195-210, 1994.
DOI : 10.1016/0167-2789(94)90210-0

C. L. Street and M. Y. Hussaini, A numerical simulation of the appearance of chaos in finite-length Taylor-Couette flow, Applied Numerical Mathematics, vol.7, issue.1, pp.41-71, 1991.
DOI : 10.1016/0168-9274(91)90103-7

Y. Takeda, K. Kobashi, and W. E. Fischer, Observation of the transient behaviour of Taylor vortex flow between rotating concentric cylinders after sudden start, Experiments in Fluids, vol.9, issue.6, pp.9-317, 1990.
DOI : 10.1007/BF00188759

S. J. Tavener, T. Mullin, and K. A. Cliffe, Novel bifurcation phenomena in a rotating annulus, Journal of Fluid Mechanics, vol.65, issue.-1, pp.229-483, 1991.
DOI : 10.1017/S0022112074001224

G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Roy. Soc. A, pp.223-289, 1923.

C. Van-atta, Exploratory measurements in spiral turbulence, Journal of Fluid Mechanics, vol.none, issue.03, pp.495-512, 1966.
DOI : 10.1017/S0022112066000211

J. M. Vanel, R. Peyret-and-p, and . Bontoux, A pseudospectral solution of vorticity streamfunction equations suing the influence matrix technique. Numerical Methods for Fluid Dynamics II, pp.463-475, 1986.

E. Weisshaar, F. H. Busse-and-m, and . Nagata, Twist vortices and their instabilities in the Taylor???Couette system, Journal of Fluid Mechanics, vol.226, issue.-1, pp.549-564, 1991.
DOI : 10.1017/S0022112086001179

S. T. Wereley and R. M. Lueptow, Azimuthal velocity in supercritical circular Couette flow, Experiments in Fluids, vol.18, issue.1-2, pp.1-9, 1994.
DOI : 10.1007/BF00209355

S. T. Wereley and R. M. Lueptow, Spatio-temporal character of non-wavy and wavy Taylor???Couette flow, Journal of Fluid Mechanics, vol.364, pp.59-80, 1998.
DOI : 10.1017/S0022112098008969

S. C. Abrahamson, J. K. Eaton, and D. J. Koga, The flow between shrouded co-rotating disks, Phys. Fluids, pp.1-241, 1989.

S. C. Cheah, H. Iacovides, D. C. Jackson, H. E. Ji-and-b, and . Launder, Experimental investigation of enclosed rotor-stator disk flows, Experimental Thermal and Fluid Science, vol.9, issue.4, pp.445-455, 1994.
DOI : 10.1016/0894-1777(94)90022-1

J. H. Ferziger, . Milovan, and . Peri?, Computational Methods for Fluid Dynamics. 3ème édition, 2002.

T. B. Gatski and C. L. Rumsey, Linear and nonlinear eddy viscosity models. Closure Strategies for Turbulent and Transitional Flows, 2002.
DOI : 10.1017/cbo9780511755385.003

J. A. Humphrey, C. A. Schuler, and D. R. Webster, Unsteady laminar flow between a pair of disks corotating in a fixed cylindrical enclosure, Physics of Fluids, vol.7, issue.6, pp.1225-1240, 1995.
DOI : 10.1063/1.868753

H. Iacovides, D. C. Jackson, G. E. Kelemenis-and-b, and . Launder, Experiments on local heat transfer in a rotating square-ended U-bend, International Journal of Heat and Fluid Flow, vol.20, issue.3, pp.20-302, 1999.
DOI : 10.1016/S0142-727X(99)00019-3

H. Iacovides, K. S. Nikas, M. A. Te, and . Braak, Turbulent flow computations in rotating cavities using low-Reynolds-Number models. ASME Paper 96-GT- 159, International Gas Turbine and Aeroengine Congress & Exhibition, 1996.

H. Iacovides and I. P. Theofanopoulos, Turbulence modeling of axisymmetric flow inside rotating cavities, International Journal of Heat and Fluid Flow, vol.12, issue.1, pp.2-11, 1991.
DOI : 10.1016/0142-727X(91)90002-D

M. Ito, Y. Yamada, S. Imao-and-m, and . Gouda, Experiments on turbulent flow due to an enclosed rotating disc, Proceedings 1 st Symposium on Engineering Turbulence Modelling and Measurements, pp.659-668, 1990.

R. C. Kloosterziel and G. J. Van-heijst, An experimental study of unstable barotropic vortices in a rotating fluid, Journal of Fluid Mechanics, vol.35, issue.-1, pp.1-24, 1991.
DOI : 10.1063/1.864781

M. Lygren and H. I. Anderson, Turbulent flow between a rotating and a stationary disk, Journal of Fluid Mechanics, vol.426, pp.297-326, 2001.
DOI : 10.1017/S0022112000002287

A. P. Morse, Numerical Prediction of Turbulent Flow in Rotating Cavities, Journal of Turbomachinery, vol.110, issue.2, pp.131-138, 1991.
DOI : 10.1115/1.3262181

J. M. Owen, Flow and Heat Transfer in Rotating-Disc Systems, Proceedings of the 1992 International Symposium on Heat Transfer in Turbomachinery, pp.33-58, 2000.
DOI : 10.1615/ICHMT.1994.IntSympHetatTransTurb.140

R. Schiestel, Les écoulements turbulents. Modélisation et simulation, Editions Hermes, 1998.

E. Serre, P. E. Bontoux-and-b, and . Launder, Direct numerical simulation of transitional turbulent flow in a closed rotor-stator cavity, Flow, Turbulence and Combustion, vol.69, issue.1, pp.35-50, 2002.
DOI : 10.1023/A:1022467232348

P. G. Tucker, The temporal behaviour of flow in rotating cavities Advances in computational heat transfert, pp.655-662, 2001.