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.

Mot clés : Mécanique des fluides numérique, Transitions, Convection thermique

Marcello Lappa ^{1, 2}

@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] 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] 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] On the stability of plane-parallel advective flows in long horizontal layers, Microgravity Q., Volume 2 (1992) no. 3, pp. 141-151

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

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

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

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

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

[11] Stability of multiple steady states of convection in laterally heated cavities, J. Fluid Mech., Volume 388 (1999), pp. 315-334

[12] Non-symmetric convective flows in laterally heated rectangular cavities, Int. J. Comput. Fluid Dynam., Volume 11 (1999), pp. 261-273

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

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

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

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

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

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

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

[21] On oscillatory instability of plane-parallel convective motion in a vertical channel, J. Appl. Math. Mech., Volume 36 (1972), pp. 707-710

[22] 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] Secondary convective steady motions in a plane vertical fluid layer, Mekh. Zhid. Gaza, Volume 5 (1968), pp. 130-136

[24] 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] Natural convection in a vertical slot: accurate solution of the linear stability equations, ANZIAM J., Volume 45 (2004), p. C92-C105 (E)

[26] 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] 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] 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] Convection and instabilities in differentially heated inclined shallow rectangular boxes, C. R. Acad. Sci. IIB, Volume 36 (1998), pp. 711-718

[30] 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] Liquid particles tracing in three-dimensional buoyancy-driven flows, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 189-199

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

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

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

[35] 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] An experimental study of oscillatory convection in liquid gallium, J. Fluid Mech., Volume 327 (1996), pp. 199-219

[37] Spectral simulations of oscillatory convection at low Prandtl number, Int. J. Numer. Meth. Fluids, Volume 10 (1990), pp. 481-517

[38] 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] 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] Studies of buoyancy driven convection in a vertical cylinder with parabolic temperature profile, J. Cryst. Growth, Volume 97 (1989), pp. 9-17

[41] Axisymmetry breaking instabilities of natural convection in a vertical Bridgman growth configuration, J. Cryst. Growth, Volume 220 (2000), pp. 316-325

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

[43] 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] Thermocapillary flow and phase change in some widespread materials processes, Fluid Dynam. Mater. Process., Volume 1 (2005), pp. 81-95

[45] 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] 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] 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] Numerical simulation of CZ crystal growth of oxide, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 45-62

[49] Convective instability in annular pools, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 153-166

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

[51] 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] 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] Numerical study of low frequency g-jitter effect on thermal diffusion, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 4, pp. 315-328

[54] 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] Some thermal modulation effects on directional solidification, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 191-202

[56] 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] Electromagnetic stirring in crystal growth processes, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 119-126

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

[59] 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] 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] 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] 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] A model for electromagnetic control of buoyancy driven convection in glass melts, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 3, pp. 247-266

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