Geodesic
Linear stability bounds in a convection problem for variable gravity field
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 51-56 
Ioana Dragomirescu; Adelina Georgescu. Linear stability bounds in a convection problem for variable gravity field. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 51-56. http://geodesic.mathdoc.fr/item/BASM_2006_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A problem governing the convection-conduction in a horizontal layer bounded by rigid walls of a fluid heated from below for a linearly decreasing across the layer gravity field is reformulated as a variational problem. Stability bounds from the case of classical convection [1] and the case of convection in a linearly decreasing across the layer gravity field are compared. The new criterion, which yields good stability bounds for the stability limit, is shown by the numerical evaluations obtained in [2–4].

[1] Chandrasekhar S., Hydrodynamic and hydromagnetic stability, Clarendon, Oxford, 1961 | MR | Zbl

[2] Dragomirescu I., “Bounds for the onset of a convection in a variable gravity field by using isoperimetric inequalities”, International Conference “Several Aspects of Biology, Chemistry, Informatics, Mathematics and Physics” (Oradea, November 11–13, 2005)

[3] Dragomirescu I., “Linear stability for a convection problem for a variable gravity field”, Proceedings of APLIMAT 2006, Bratislava, 231–236

[4] Dragomirescu I., “Approximate neutral surface of a convection problem for variable gravity field”, Rend. Sem. Mat. Univ. Pol. Torino, 64 (2006) | MR | Zbl

[5] Herron I., “On the principle of exchange of stabilities in Rayleigh-Bénard convection”, SIAM J. Appl. Math., 61:4 (2000), 1362–1368 | DOI | MR | Zbl

[6] Joseph D. D., “Eigenvalue bounds for the Orr-Sommerfeld equation”, J. Fluid Mech., 33:3 (1968), 617–621 | DOI | MR | Zbl

[7] Straughan B., The energy method, stability, and nonlinear convection, 2nd ed., Springer, Berlin, 2003 | MR