Comptes Rendus
Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 2: lateral heating and the Hadley circulation
Comptes Rendus. Mécanique, Volume 335 (2007) no. 5-6, pp. 261-268.

The focused discussion limited in Part 1 (C. R. Mecanique, this issue) to systems heated from below is now extended to the case of laterally heated configurations and the related problem of the Hadley flow stability.

La première partie 1 (C. R. Mecanique, ce numéro) de cette discussion restreinte aux systèmes de chauffage est ici étendue aux cas des configurations chauffées latéralement et au problème de la stabilité de l'écoulement de Hadley.

Published online:
DOI: 10.1016/j.crme.2007.05.004
Keywords: Computational fluid dynamic, Thermal convection, Transitions
Mot clés : Mécanique des fluides numérique, Transitions, Convection thermique

Marcello Lappa 1, 2

1 MARS (Microgravity Advanced Research and Support) Center, Via Gianturco 31, 80146 Napoli, Italy
2 Via Salvator Rosa 53, 80046 San Giorgio a Cremano (Na), Italy
@article{CRMECA_2007__335_5-6_261_0,
     author = {Marcello Lappa},
     title = {Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. {Part} 2: lateral heating and the {Hadley} circulation},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {261--268},
     publisher = {Elsevier},
     volume = {335},
     number = {5-6},
     year = {2007},
     doi = {10.1016/j.crme.2007.05.004},
     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 2: lateral heating and the Hadley circulation
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 261
EP  - 268
VL  - 335
IS  - 5-6
PB  - Elsevier
DO  - 10.1016/j.crme.2007.05.004
LA  - en
ID  - CRMECA_2007__335_5-6_261_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 2: lateral heating and the Hadley circulation
%J Comptes Rendus. Mécanique
%D 2007
%P 261-268
%V 335
%N 5-6
%I Elsevier
%R 10.1016/j.crme.2007.05.004
%G en
%F CRMECA_2007__335_5-6_261_0
Marcello Lappa. Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 2: lateral heating and the Hadley circulation. Comptes Rendus. Mécanique, Volume 335 (2007) no. 5-6, pp. 261-268. doi : 10.1016/j.crme.2007.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.05.004/

[1] M. Lappa 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] M. Lappa 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] E. Semma; M. El Ganaoui; A. Cheddadi; P. Bontoux Etude numérique des instabilités de la phase fluide et de l'interface de solidification en croissance dirigée horizontale, C. R. Acad. Sci. Paris, Volume 331 (2003), pp. 631-639

[4] G.Z. Gershuni; P. Laure; V.M. Myznikov; B. Roux; E.M. Zhukhovitsky On the stability of plane-parallel advective flows in long horizontal layers, Microgravity Q., Volume 2 (1992) no. 3, pp. 141-151

[5] H.P. Kuo; S.A. Korpela Stability and finite amplitude natural convection in a shallow cavity with insulated top and bottom and heated from the side, Phys. Fluids, Volume 31 (1988), pp. 33-42

[6] J.E. Hart Stability of thin non-rotating Hadley circulations, J. Atmos. Sci., Volume 29 (1972), pp. 687-697

[7] J.E. Hart A note on the stability of low-Prandtl-number Hadley circulations, J. Fluid Mech., Volume 132 (1983), pp. 271-281

[8] A.E. Gill A theory of thermal oscillations in liquid metals, J. Fluid Mech., Volume 64 (1974) no. 3, pp. 577-588

[9] P. Laure Study of convective motion in a rectangular cavity with horizontal temperature gradient, J. Méc. Théor. Appl., Volume 6 (1987), pp. 351-382

[10] B. Roux; H. Ben Hadid; P. Laure Hydrodynamical regimes in metallic melts subject to a horizontal temperature gradient, Eur. J. Mech. B/Fluids, Volume 8 (1989), pp. 375-396

[11] A.Yu. Gelfgat; P.Z. Bar-Yoseph; A.L. Yarin Stability of multiple steady states of convection in laterally heated cavities, J. Fluid Mech., Volume 388 (1999), pp. 315-334

[12] A.Yu. Gelfgat; P.Z. Bar-Yoseph; A.L. Yarin Non-symmetric convective flows in laterally heated rectangular cavities, Int. J. Comput. Fluid Dynam., Volume 11 (1999), pp. 261-273

[13] R. Delgado-Buscalioni Convection patterns in end-heated inclined enclosures, Phys. Rev. E, Volume 64 (2001), p. 016303 (17 pp)

[14] J.C. Patterson; J. Imberger Unsteady natural convection in a rectangular cavity, J. Fluid Mech., Volume 100 (1980), pp. 65-86

[15] J.C. Patterson; S.W. Armfield Transient features of natural convection in a cavity, J. Fluid Mech., Volume 219 (1990), pp. 469-497

[16] S.G. Schladow Oscillatory motion in a side-heated cavity, J. Fluid Mech., Volume 213 (1990), pp. 589-610

[17] J.C. Patterson; J. Imberger Unsteady natural convection in a rectangular cavity, J. Fluid Mech., Volume 100 (1980), pp. 65-86

[18] J.C. Patterson; S.W. Armfield Transient features of natural convection in a cavity, J. Fluid Mech., Volume 219 (1990), pp. 469-497

[19] G.K. Batchelor Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Quart. Appl. Math., Volume 12 (1954), pp. 209-233

[20] R.V. Birikh On small perturbations of a plane parallel flow with cubic velocity profile, J. Appl. Math. Mech., Volume 30 (1966), pp. 432-438

[21] R.V. Birikh; G.Z. Gershuni; E.M. Zhukhovitskii; R.N. Rudakov On oscillatory instability of plane-parallel convective motion in a vertical channel, J. Appl. Math. Mech., Volume 36 (1972), pp. 707-710

[22] S.A. Korpela; D. Gözüm; C.B. Baxi On the stability of the conduction regime of natural convection in a vertical slot, Int. J. Heat Mass Transfer, Volume 16 (1973) no. 9, pp. 1683-1690

[23] G.Z. Gershuni; E.M. Zhukhovitskii; E.L. Tarunin Secondary convective steady motions in a plane vertical fluid layer, Mekh. Zhid. Gaza, Volume 5 (1968), pp. 130-136

[24] K. Fujimura; J. Mizushima Nonlinear equilibrium solutions for traveling waves in free convection between vertical parallel plates, Eur. J. Mech. B Fluids, Volume 10 (1991) no. Suppl. 2, pp. 25-30

[25] G.D. McBain; S.W. Armfield Natural convection in a vertical slot: accurate solution of the linear stability equations, ANZIAM J., Volume 45 (2004), p. C92-C105 (E)

[26] R.M. Clever; F.H. Busse Tertiary and quarternary solutions for convection in a vertical fluid layer heated from the side, Chaos Solitons Fractals, Volume 5 (1995), pp. 1795-1803

[27] A.Yu. Gelfgat Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method, Int. J. Numer. Meth. Fluids, Volume 44 (2004), pp. 135-146

[28] D.A. Bratsun; A.V. Zyuzgin; G.F. Putin Non-linear dynamics and pattern formation in a vertical fluid layer heated from the side, Int. J. Heat Fluid Flow, Volume 24 (2003) no. 6, pp. 835-852

[29] R. Delgado-Buscalioni; E. Crespo del Arco; P. Bontoux; J. Ouazzani Convection and instabilities in differentially heated inclined shallow rectangular boxes, C. R. Acad. Sci. IIB, Volume 36 (1998), pp. 711-718

[30] R. Delgado-Buscalioni; E. Crespo del Arco Stability of thermally driven shear flows in long inclined cavities with end-to-end temperature gradient, Int. J. Heat Mass Transfer, Volume 42 (1999), pp. 2811-2822

[31] D.E. Melnikov; V.M. Shevtsova Liquid particles tracing in three-dimensional buoyancy-driven flows, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 189-199

[32] M. Afrid; A. Zebib Oscillatory three dimensional convection in rectangular cavities and enclosures, Phys. Fluids, Volume 2 (1990) no. 8, pp. 1318-1327

[33] J.M. Pratte; J.E. Hart Endwall driven, low Prandtl number convection in a shallow rectangular cavity, J. Cryst. Growth, Volume 102 (1990), pp. 54-68

[34] M.C. Hung; C.D. Andereck Transitions in convection driven by a horizontal temperature gradient, Phys. Lett. A, Volume 132 (1988), pp. 253-258

[35] R. Delgado-Buscalioni; E. Crespo del Arco; P. Bontoux Flow transitions of a low-Prandtl-number fluid in an inclined 3D cavity, Eur. J. Mech. B Fluids, Volume 329 (2001), pp. 1-17

[36] M.G. Braunsfurth; T. Mullin An experimental study of oscillatory convection in liquid gallium, J. Fluid Mech., Volume 327 (1996), pp. 199-219

[37] J.P. Pulicani; E. Crespo del Arco; A. Randriampianina; P. Bontoux; R. Peyret Spectral simulations of oscillatory convection at low Prandtl number, Int. J. Numer. Meth. Fluids, Volume 10 (1990), pp. 481-517

[38] P. Bontoux; B. Roux; G.H. Schiroky; B.L. Markham; F. Rosenberger Convection in the vertical midplane of a horizontal cylinder. Comparison of two-dimensional approximations with three-dimensional results, Int. J. Heat Mass Transfer, Volume 29 (1986) no. 2, pp. 227-240

[39] S. Xin; P. Le Quéré; O. Daube Natural convection in a differentially heated horizontal cylinder: Effects of Prandtl number on flow structure and instability, Phys. Fluids, Volume 9 (1997) no. 4, pp. 1014-1033

[40] J. Baumgartl; W. Budweiser; G. Muller; G. Neumann Studies of buoyancy driven convection in a vertical cylinder with parabolic temperature profile, J. Cryst. Growth, Volume 97 (1989), pp. 9-17

[41] A.Yu. Gelfgat; P.Z. Bar-Yoseph; A. Solan Axisymmetry breaking instabilities of natural convection in a vertical Bridgman growth configuration, J. Cryst. Growth, Volume 220 (2000), pp. 316-325

[42] R. Selver; Y. Kamotani; S. Ostrach Natural convection of a liquid metal in vertical cylinders heated locally from the side, J. Heat Transfer, Volume 120 (1998), pp. 108-114

[43] D.J. Ma; D. Henry; H. Ben Hadid Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side, Phys. Fluids, Volume 17 (2005) no. 12, p. 124101 (12 pp)

[44] G. Amberg; J. Shiomi Thermocapillary flow and phase change in some widespread materials processes, Fluid Dynam. Mater. Process., Volume 1 (2005), pp. 81-95

[45] M. Lappa Review: Possible strategies for the control and stabilization of Marangoni flow in laterally heated floating zones, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 171-188

[46] A.Yu. Gelfgat; A. Rubinov; P.Z. Bar-Yoseph; A. Solan On the three-dimensional instability of thermocapillary convection in arbitrarily heated floating zones in microgravity environment, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 21-32

[47] C.W. Lan; B.C. Yeh Effects of rotation on heat flow, segregation, and zone shape in a small-scale floating-zone silicon growth under axial and transversal magnetic fields, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 33-44

[48] T. Tsukada; M. Kobayashi; C.J. Jing; N. Imaishi Numerical simulation of CZ crystal growth of oxide, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 45-62

[49] Y.R. Li; L. Peng; W.Y. Shi; N. Imaishi Convective instability in annular pools, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 153-166

[50] K. Matsunaga; H. Kawamura Influence of thermocapillary convection on solid–liquid interface, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 1, pp. 59-64

[51] M. El-Gamma; J.M. Floryan Thermocapillary effects in systems with variable liquid mass exposed to concentrated heating, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 1, pp. 17-26

[52] K. Achour; S. Kaddeche; A. Gharbi; H. Ben Hadid; D. Henry On the stability of the Hadley flow under the action of an acoustic wave, Fluid Dynam. Mater. Process., Volume 1 (2006) no. 4, pp. 277-284

[53] Y. Yan; V. Shevtsova; M.Z. Saghir Numerical study of low frequency g-jitter effect on thermal diffusion, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 4, pp. 315-328

[54] V.G. Kozlov; N.V. Selin Pendulum thermal vibrational convection in a liquid layer with internal heat generation, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 107-118

[55] E.A. Semma; M. El Ganaoui; V. Timchenko; E. Leonardi Some thermal modulation effects on directional solidification, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 191-202

[56] Y. Okano; A. Ishii; H. Miyashita; H. Minakuchi; S. Dost A numerical study of controlling the g-jitter induced convection in the solution of a crystal growth crucible under microgravity, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 4, pp. 261-270

[57] N. Ma; J.S. Walker Electromagnetic stirring in crystal growth processes, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 119-126

[58] K. Kakimoto; L. Liu Flow instability of silicon melt in magnetic fields, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 167-174

[59] M. Sohail; M.Z. Saghir Three-dimensional modeling of the effects of misalignment on the growth of Ge1-xSix by the traveling solvent method, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 127-140

[60] T.J. Jaber; M.Z. Saghir The effect of rotating magnetic fields on the growth of SiGe using the traveling solvent method, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 175-190

[61] M. Mosaad; A. Ben-Nakhi; M.H. Al-Hajeri Thermal communication between two vertical systems of free and forced convection via heat conduction across a separating wall, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 4, pp. 301-314

[62] N.I. Wakayama; D.C. Yin; J.W. Qi How does buoyancy-driven convection affect biological macromolecular crystallization? An analysis of microgravity and hypergravity effects by means of magnetic field gradients, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 153-170

[63] C. Giessler; C. Sievert; U. Krieger; B. Halbedel; D. Huelsenberg; U. Luedke; A. Thess A model for electromagnetic control of buoyancy driven convection in glass melts, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 3, pp. 247-266

Cited by Sources:

Comments - Policy