Geodesic
Amplitude equations for three-dimensional double-diffusive convection in the neighborhood of Hopf bifurcation points
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2008), pp. 46-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Three dimensional double-diffusive convection in a horizontally infinite layer of an uncompressible liquid is considered in the neighborhood of Hopf bifurcation points. A system of amplitude equations for horizontal variations of the amplitude of a square type convective cells is derived by multiple-scale method. An attention is paid to an interaction of convection and horizontal curl. Different cases of the derived equations are discussed.
Mots-clés : double-diffusive convection, amplitude equations
Keywords: multiple-scale method. 
@article{VUU_2008_3_a5,
     author = {S. B. Kozitskii},
     title = {Amplitude equations for three-dimensional double-diffusive convection in the neighborhood of {Hopf} bifurcation points},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {46--60},
     year = {2008},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2008_3_a5/}
}
TY  - JOUR
AU  - S. B. Kozitskii
TI  - Amplitude equations for three-dimensional double-diffusive convection in the neighborhood of Hopf bifurcation points
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2008
SP  - 46
EP  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2008_3_a5/
LA  - ru
ID  - VUU_2008_3_a5
ER  - 
%0 Journal Article
%A S. B. Kozitskii
%T Amplitude equations for three-dimensional double-diffusive convection in the neighborhood of Hopf bifurcation points
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2008
%P 46-60
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2008_3_a5/
%G ru
%F VUU_2008_3_a5
S. B. Kozitskii. Amplitude equations for three-dimensional double-diffusive convection in the neighborhood of Hopf bifurcation points. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2008), pp. 46-60. http://geodesic.mathdoc.fr/item/VUU_2008_3_a5/

[1] Khappert G., Terner Dzh., “Konvektsiya, obuslovlennaya dvoinoi diffuziei”, Sovremennaya gidrodinamika. Uspekhi i problemy, Mir, M., 1984, 413–453

[2] Terner Dzh., Effekty plavuchesti v zhidkostyakh, Mir, M., 1977, 431 pp.

[3] Kozitskii S. B., “Amplitudnye uravneniya dlya sistemy s termokhalinnoi konvektsiei”, PMTF, 41:2 (2000), 56–66 | MR

[4] Balmforth N. J. and J. A. Biello, “Double diffusive instability in a tall thin slot”, J. Fluid Mech., 375 (1998), 203–233 | DOI | MR | Zbl

[5] Getling A. V., Konvektsiya Releya–Benara. Struktury i dinamika, Editorial URSS, M., 1999, 247 pp.

[6] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1988, 736 pp. | MR

[7] A. Sorkin, V. Sorkin, I. Leizerson, “Salt fingers in double-diffusive systems”, Physica A, 303 (2002), 13–26 | DOI

[8] Knobloch E., Moore D. R., Toomre J. and Weiss N. O., “Transitions to chaos in two-dimensional double-diffusive convection”, J. Fluid Mech., 166 (1986), 409–448 | DOI | MR | Zbl

[9] Weiss N. O., “Convection in an imposed magnetic field. Part 1. The development of nonlinear convection”, J. Fluid Mech., 108 (1981), 247–272 | DOI | Zbl

[10] Weiss N. O., “Convection in an imposed magnetic field. Part 2. The dynamical regime”, J. Fluid Mech., 108 (1981), 273–289 | DOI | Zbl

[11] Dodd R., Eilbek Dzh., Gibbon Dzh., Morris Kh., Solitony i nelineinye volnovye uravneniya, Mir, M., 1988, 694 pp. | MR

[12] Nayfeh A. H., Perturbation methods, John Wiley and Sons, New York, London, Sydney, Toronto, 1973 | MR | Zbl

[13] Nayfeh A. H., Introduction to perturbation techniques, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, 1981 | MR | Zbl

[14] Kozitskiy S. B., “Fine structure generation in double-diffusive system”, Phys. Rev. E, 72:5 (2005), 056309, 6 pp. | DOI