R. E. Powe, C. T. Carley, and E. H. Bishop, Free Convective Flow Patterns in Cylindrical Annuli, Journal of Heat Transfer, vol.91, issue.3, pp.310-314, 1969.
DOI : 10.1115/1.3580158

E. H. Bishop, C. T. Carley, and R. E. Powe, Natural convective oscillatory flow in cylindrical annuli, International Journal of Heat and Mass Transfer, vol.11, issue.12, pp.1741-1752, 1968.
DOI : 10.1016/0017-9310(68)90017-3

Y. F. Rao, Y. Miki, K. Fukuda, Y. Takata, and S. Hasegawa, Flow patterns of natural convection in horizontal cylindrical annuli, International Journal of Heat and Mass Transfer, vol.28, pp.705-714, 1985.

K. Vafai and J. Ettefagh, An investigation of transient three-dimensional buoyancy-driven flow and heat transfer in a closed horizontal annulus, International Journal of Heat and Mass Transfer, vol.34, issue.10, pp.2555-2569, 1991.
DOI : 10.1016/0017-9310(91)90096-W

P. Cadiou, ContributionàContributionà l'´ etude numérique des transferts de chaleur par convection naturelle ou par convection mixte dans une cavité annulaire horizontale, 1997.

M. P. Dyko, K. Vafai, and A. K. Mojtabi, A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus, Journal of Fluid Mechanics, vol.381, pp.27-61, 1999.
DOI : 10.1017/S0022112098002948

M. P. Dyko and K. Vafai, Three-dimensional natural convective states in a narrow-gap horizontal annulus, Journal of Fluid Mechanics, vol.445, pp.1-36, 2001.
DOI : 10.1017/S0022112001005067

M. P. Dyko and K. Vafai, On the presence of odd transverse convective rolls in narrow-gap horizontal annuli, Physics of Fluids, vol.34, issue.3, pp.1291-1294, 2002.
DOI : 10.1017/S0022112072000898

J. Y. Choi and M. Kim, Three-dimensional linear stability of natural convective flow between concentric horizontal cylinders, International Journal of Heat and Mass Transfer, vol.36, issue.17, pp.4173-4180, 1993.
DOI : 10.1016/0017-9310(93)90079-L

J. Yoo, Dual steady solutions in natural convection between horizontal concentric cylinders, International Journal of Heat and Fluid Flow, vol.17, issue.6, pp.587-593, 1996.
DOI : 10.1016/S0142-727X(96)00064-1

J. Yoo, Dual free-convective flows in a horizontal annulus with a constant heat flux wall, International Journal of Heat and Mass Transfer, vol.46, issue.13, pp.2499-2503, 2003.
DOI : 10.1016/S0017-9310(02)00539-2

P. Cadiou, G. Desrayaud, and G. Lauriat, Natural Convection in a Narrow Horizontal Annulus: The Effects of Thermal and Hydrodynamic Instabilities, Journal of Heat Transfer, vol.120, issue.4, pp.1019-1026, 1998.
DOI : 10.1115/1.2825885

P. Cadiou, G. Desrayaud, and G. Lauriat, Etude numérique de la stabilité desécoulementsdesécoulements de convection naturelle dans des espaces annulaires horizontaux de faiblé epaisseur, Comptes Rendus de l' Academie des Sciences Serie IIb:Mecanique Physique Chimie Astronomie, pp.119-124, 1999.
DOI : 10.1016/s1287-4620(99)80020-9

G. Desrayaud, G. Lauriat, and P. Cadiou, Thermoconvective instabilities in a narrow horizontal air-filled annulus, International Journal of Heat and Fluid Flow, vol.21, issue.1, pp.65-73, 2000.
DOI : 10.1016/S0142-727X(99)00048-X

J. Mizushima and S. Hayashi, Exchange of instability modes for natural convection in a narrow horizontal annulus, Physics of Fluids, vol.73, issue.1, pp.99-106, 2001.
DOI : 10.1017/S0022112098002948

J. Mizushima, S. Hayashi, and T. Adachi, Transitions of natural convection in a horizontal annulus, International Journal of Heat and Mass Transfer, vol.44, issue.6, pp.1249-1257, 2001.
DOI : 10.1016/S0017-9310(00)00188-5

G. Petrone, E. Chénier, G. Lauriat, and G. Desrayaud, Brisure de symétrie desécoulementsdesécoulements de convection naturelle entre deux cylindres coaxiaux horizontaux, Thermique et microtechnologie. Congrès Français de Mécanique, 2003.

G. Petrone, E. Chénier, and G. Lauriat, Instabilities of two dimensional natural convection in a horizontal annulus, Heat Transfer in unsteady and transitional flows, pp.27-32, 2003.

G. Karniadakis, M. Israeli, and S. Orsag, High-order splitting methods for the incompressible Navier-Stokes equations, Journal of Computational Physics, vol.97, issue.2, pp.414-443, 1991.
DOI : 10.1016/0021-9991(91)90007-8

W. E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quarterly of Applied Mathematics, vol.9, issue.1, pp.17-29, 1951.
DOI : 10.1090/qam/42792

C. K. Mamun and L. S. Tuckerman, Asymmetry and Hopf bifurcation in spherical Couette flow, Physics of Fluids, vol.9, issue.1, pp.80-91, 1995.
DOI : 10.1007/BF01032401

E. Chénier, C. Delcarte, and G. Labrosse, Stability of the axisymmetric buoyant-capillary flows in a laterally heated liquid bridge, Physics of Fluids, vol.9, issue.3, pp.527-541, 1999.
DOI : 10.1051/epjap:1998169

A. Griewank and G. Reddien, The Calculation of Hopf Points by a Direct Method, IMA Journal of Numerical Analysis, vol.3, issue.3, pp.295-303, 1983.
DOI : 10.1093/imanum/3.3.295

P. Joly and R. Eymard, Preconditioned biconjugate gradient methods for numerical reservoir simulation Laboratoire d'analyse numérique de l'université Pierre et Marie Curie, 1988.
DOI : 10.1016/0021-9991(90)90039-4

V. Frayssé, L. Giraud, S. Gratton, and J. Langou, A set of GMRES routines for real and complex arithmetics on high performance computers, CERFACS, vol.3, 2003.

E. Chénier, Etude de la stabilité linéaire desécoulementsdesécoulements thermocapillaires et thermogravitationnels en croissance cristalline, 1997.

A. Cheddadi, J. P. Caltagirone, A. Mojtabi, and K. Vafai, Free Two-Dimensional Convective Bifurcation in a Horizontal Annulus, Journal of Heat Transfer, vol.114, issue.1, pp.99-106, 1992.
DOI : 10.1115/1.2911274

C. J. Kim and S. T. Ro, Numerical investigation on bifurcative natural convection in an air-filled horizontal annulus, Proc. 10th Int. Heat Transfer Conference, pp.85-90, 1994.

J. D. Chung, C. J. Kim, H. Yoo, and J. S. Lee, Numerical investigation on the bifurcative natural convection in a horizontal concentric annulus, Numerical Heat Transfer Part A, vol.36, pp.291-30729, 1999.

G. Petrone, Bifurcations Saddle-node Virtual trancritical imperfect pitchfork, p.1894, 1914.

G. Petrone, 16 Elements of the bifurcation diagrams at R = 1.24 and R = 1.25. The arrows indicate the part of the curves coming closer with the increasing radius ratio