[Instabilités secondaires et oscillatoires dans des modèles 3D canoniques pour la croissance cristalline. 1ère partie : des systèmes Rayleigh–Bénard]
Les instabilités secondaires et oscillatoires pour la convection gravitationnelle thermique ont fait l'objet d'études intensives durant les dernières années du fait de leur pertinence en science des matériaux, et plus particulièrement dans le domaine de la croissance cristalline. Le but de la présente discussion est de fournir une revue comparative et critique du sujet par l'examen des études existantes et de contributions très récentes. Il complète les précédentes revues (Lappa, 2005) qui ont été restreintes à la brisure de symétrie tridimensionnelle dans le cas stationnaire et/ou à la première bifurcation de l'écoulement.
Secondary and oscillatory instabilities in thermal gravitational convection have been the focus of intensive studies over recent years due to their relevance in materials science, and in particular, in the field of crystal growth from the melt. The purpose of the present discussion is to provide a comparative and critical review of the subject through examination of existing studies and very recent contributions. It complements earlier reviews (Lappa, 2005) that were limited to the survey of steady three-dimensional symmetry breaking effects and/or the primary bifurcation of the flow.
Mot clés : Mécanique des fluides numérique, Transitions, Convection thermique
@article{CRMECA_2007__335_5-6_253_0,
author = {Marcello Lappa},
title = {Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. {Part} 1: {Rayleigh{\textendash}B\'enard} systems},
journal = {Comptes Rendus. M\'ecanique},
pages = {253--260},
publisher = {Elsevier},
volume = {335},
number = {5-6},
year = {2007},
doi = {10.1016/j.crme.2007.05.003},
language = {en},
}
TY - JOUR AU - Marcello Lappa TI - Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 1: Rayleigh–Bénard systems JO - Comptes Rendus. Mécanique PY - 2007 SP - 253 EP - 260 VL - 335 IS - 5-6 PB - Elsevier DO - 10.1016/j.crme.2007.05.003 LA - en ID - CRMECA_2007__335_5-6_253_0 ER -
%0 Journal Article %A Marcello Lappa %T Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 1: Rayleigh–Bénard systems %J Comptes Rendus. Mécanique %D 2007 %P 253-260 %V 335 %N 5-6 %I Elsevier %R 10.1016/j.crme.2007.05.003 %G en %F CRMECA_2007__335_5-6_253_0
Marcello Lappa. Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 1: Rayleigh–Bénard systems. Comptes Rendus. Mécanique, Volume 335 (2007) no. 5-6, pp. 253-260. doi : 10.1016/j.crme.2007.05.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.05.003/
[1] Thermal convection and related instabilities in models of crystal growth from the melt on earth and in microgravity: Past history and current status, Cryst. Res. Technol., Volume 40 (2005) no. 6, pp. 531-549
[2] On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 1-19
[3] Different modes of Rayleigh–Bénard instability in two- and three-dimensional rectangular enclosures, J. Comput. Phys., Volume 156 (1999), pp. 300-324
[4] On the onset of free convection in a rectangular channel, J. Non-Equilibrium Thermodynam., Volume 6 (1981), p. 141
[5] Non-stationary finite amplitude convection, J. Fluid Mech., Volume 28 (1967), pp. 223-239
[6] Many routes to turbulent convection, J. Fluid Mech., Volume 100 (1980), pp. 449-470
[7] Rayleigh–Bénard convection in a small aspect ratio enclosure: Part I—bifurcation to oscillatory convection, ASME J. Heat Transfer, Volume 115 (1993), pp. 360-366
[8] Rayleigh–Bénard convection in limited domains: Part 1—oscillatory flow, Numer. Heat Transfer Part A, Volume 36 (1999) no. 1, pp. 1-16
[9] Crossed rolls at onset of convection in a rigid box, J. Fluid Mech., Volume 191 (1988), pp. 583-597
[10] Rayleigh–Bénard convection in an intermediate aspect ratio rectangular container, J. Fluid Mech., Volume 163 (1986), pp. 195-226
[11] The Rayleigh–Bénard problem in intermediate bounded domain, J. Fluid Mech., Volume 254 (1993), pp. 375-400
[12] Temporal, spatial and thermal features of 3-D Rayleigh–Bénard convection by a least-squares finite element method, Comput. Methods Appl. Mech. Engrg., Volume 140 (1997), pp. 201-219
[13] Pattern selection for Rayleigh–Bénard convection in intermediate aspect ratio boxes, Numer. Heat Transfer Part A, Volume 27 (1995) no. 6, pp. 621-637
[14] Transition to time-dependent convection, J. Fluid Mech., Volume 65 (1974), pp. 625-645
[15] Rayleigh–Bénard convection in a small aspect ratio enclosure: Part II—bifurcation to chaos, ASME J. Heat Transfer, Volume 115 (1993), pp. 367-376
[16] The oscillatory instability of convection rolls in a low Prandtl number fluid, J. Fluid Mech., Volume 52 (1972), pp. 97-112
[17] Oscillatory and collective instabilities in large Prandtl number convection, J. Fluid Mech., Volume 66 (1974), pp. 67-79
[18] Some further studies on the transition to turbulent convection, J. Fluid Mech., Volume 60 (1973), pp. 285-303
[19] Numerical simulation of the Rayleigh–Bénard convection of air in a box of a large aspect ratio, Phys. Fluids, Volume 11 (1999), pp. 743-745
[20] Buoyancy-driven flow transitions in deep cavities heated from below, J. Heat Transfer, Volume 124 (2002) no. 4, pp. 650-659
[21] Rayleigh–Bénard convection in limited domains: Part 2—transition to chaos, Numer. Heat Transfer Part A, Volume 36 (1999) no. 1, pp. 17-34
[22] On the thermoconvective instability in a bounded cylindrical fluid layer, Int. J. Heat Mass Transfer, Volume 14 (1971), pp. 2157-2160
[23] The effect of wall conduction on the stability of a fluid in a right circular cylinder heated from below, Trans. ASME J. Heat Transfer, Volume 105 (1983), pp. 255-260
[24] Flow state multiplicity in convection, Phys. Fluids, Volume 11 (1999), pp. 2815-2817
[25] Numerical study of Rayleigh–Bénard convection in a cylinder, Numer. Heat Transfer Part A, Volume 41 (2002), pp. 673-683
[26] On the onset of convective instabilities in cylindrical cavities heated from below, I. Pure thermal case. Phys. Fluids, Volume 11 (1999) no. 8, pp. 2078-2088
[27] Natural convection in vertical Bridgman configurations, J. Cryst. Growth, Volume 70 (1984), pp. 78-93
[28] Convection transitions within a vertical cylinder heated from below, Phys. Fluids, Volume 29 (1986) no. 7, pp. 2028-2031
[29] Numerical simulations and analysis of axisymmetric convection in a vertical cylinder: An effect of Prandtl number, Phys. Fluids A, Volume 1 (1989), pp. 1348-1359
[30] Three-dimensional numerical simulation of buoyancy driven convection in vertical cylinders heated from below, J. Fluid Mech., Volume 214 (1990), pp. 559-578
[31] Dynamics and selection of giant spirals in Rayleigh–Bénard convection, Phys. Rev. Lett., Volume 81 (1998), pp. 5334-5337
[32] Pattern formation in Rayleigh–Bénard convection in a cylindrical container, Phys. Rev. E, Volume 62 (2000), pp. 4927-4931
[33] Rayleigh–Bénard convective structures in a cylindrical container, J. Phys., Volume 44 (1986), pp. 293-301
[34] Global bifurcation to travelling waves in axisymmetric convection, Phys. Rev. Lett., Volume 61 (1988), pp. 408-411
[35] Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below, J. Fluid Mech., Volume 326 (1996), pp. 399-415
[36] Standing and travelling waves in cylindrical Rayleigh–Bénard convection, J. Fluid Mech., Volume 559 (2006), pp. 279-298
[37] Steady and oscillatory convection in vertical cylinders heated from below. Numerical simulation of asymmetric flow regimes, Adv. Space Res., Volume 8 (1988) no. 12, pp. 281-292
[38] Transitional regimes of low-Prandtl thermal convection in a cylindrical shell, Phys. Fluids, Volume 9 (1997) no. 5, pp. 1287-1295
[39] Thermal turbulence in mercury, Phys. Rev. Lett., Volume 76 (1996), pp. 1465-1468
[40] Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number, J. Fluid Mech., Volume 335 (1997), pp. 111-140
[41] Oscillatory natural convection of a liquid metal in circular cylinders, J. Heat Transfer, Volume 116 (1994), pp. 627-632
[42] Effects of anisotropy and solid/liquid thermal conductivity ratio on flow instabilities during inverted Bridgman growth, Int. J. Heat Mass Transfer, Volume 47 (2004) no. 14–16, pp. 3403-3413
[43] Symmetry breaking of melt flow typically encountered in a Bridgman configuration heated from below, Appl. Math. Model., Volume 30 (2006) no. 11, pp. 1249-1261
[44] Plumes and waves in two-dimensional turbulent thermal convection, Phys. Rev. E, Volume 60 (1999) no. 3, pp. 2957-2963
[45] Turbulent heat flow: Structures and scaling, Phys. Today, Volume 54 (2001) no. 8, pp. 34-39
[46] Large-scale velocity structures in turbulent thermal convection, Phys. Rev. E, Volume 64 (2001) no. 3, p. 036304 (13 pp)
[47] From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection, J. Fluid Mech., Volume 503 (2004), pp. 47-56
[48] Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Q. Appl. Math., Volume 12 (1954), pp. 209-233
[49] Laminar starting plumes in high-Prandtl-number fluids, J. Fluid Mech., Volume 478 (2003), pp. 287-298
[50] Four dynamical regimes for a starting plume model, Phys. Fluids, Volume 16 (2004) no. 5, pp. 1516-1531
[51] Vortical nature of thermal plumes in turbulent convection, Phys. Fluids A, Volume 5 (1993), pp. 3226-3232
Cité par Sources :
Commentaires - Politique
Marcello Lappa
C. R. Méca (2007)
Marcello Lappa
C. R. Méca (2011)
Thermocapillary convection in cylindrical liquid bridges and annuli
Bok-Cheol Sim; Abdelfattah Zebib
C. R. Méca (2004)