Geodesic
On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundary
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 4, pp. 434-444.

Voir la notice de l'article provenant de la source Math-Net.Ru

Problem on plane unidirectional two-layer flow of viscous heat-conducting fluid in microgravity is studied. There is a situation in which the flow is generated by Marangoni forces and motion of one of channel's walls only. Using the linearization method the stability of the regime is investigated. The flow crisis is induced by thermal oscillatory or monotonic waves for different wavenumber.
Mots-clés : interface
Keywords: nonisothermal flow, neutral curve. 
@article{JSFU_2011_4_4_a1,
     author = {Viktor K. Andreev and Viktoriya B. Bekezhanova},
     title = {On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundary},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {434--444},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2011_4_4_a1/}
}
TY  - JOUR
AU  - Viktor K. Andreev
AU  - Viktoriya B. Bekezhanova
TI  - On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundary
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2011
SP  - 434
EP  - 444
VL  - 4
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2011_4_4_a1/
LA  - ru
ID  - JSFU_2011_4_4_a1
ER  - 
%0 Journal Article
%A Viktor K. Andreev
%A Viktoriya B. Bekezhanova
%T On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundary
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2011
%P 434-444
%V 4
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2011_4_4_a1/
%G ru
%F JSFU_2011_4_4_a1
Viktor K. Andreev; Viktoriya B. Bekezhanova. On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundary. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 4, pp. 434-444. http://geodesic.mathdoc.fr/item/JSFU_2011_4_4_a1/

[1] L. G. Napolitano, “Plane Marangoni–Poiseuille flow two immiscible fluids”, Acta Astronautica, 7 (1980), 461–478 | DOI | Zbl

[2] D. D. aniel, M. Renardy, Y. Renardy, “Instability of the flow of two immiscible liquids with different viscousities in a pipe”, J. Fluid. Mech., 141 (1983), 309–317

[3] C. S. Yih, “Instability due to viscosity stratification”, J. Fluid Mech., 27 (1967), 337–352 | DOI | Zbl

[4] T. I. Hesla, F. R. Pranckh, L. Preziosi, “Squire's theorem for two stratified fluids”, Phys. Fluids, 29 (1986), 2808–2811 | DOI | MR | Zbl

[5] P. T. Than, F. Rosso, D. D. Joseph, “Instability of Poiseuille flow of two mmiscible liquids with different viscousities in a channel”, Int. J. Eng. Sci., 25 (1987), 189–204 | DOI | Zbl

[6] S. G. Yiantsios, B. G. Higgins, “Linear stability of plane Poiseuille flow of two superposed fluids”, Phys. Fluids, 31 (1988), 3225–3238 | DOI | MR | Zbl

[7] M. K. Smith, “The axisymmetric long-wave instability of a concentric two-phase pipe flow”, Phys. Fluids A, 1 (1989), 494–506 | DOI | Zbl

[8] B. S. Tilley, S. H. Davis, S. G. Bankoff, “Linear stability theory of two-layer fluid flow in an inclined channel”, Phys. Fluids, 1:12 (1994), 3906–3922 | DOI | MR | Zbl

[9] B. B. Bekezhanova, “Konvektivnaya neustoichivost techeniya Marangoni–Puazeilya pri nalichii prodolnogo gradienta temperatury”, PMTF, 52:1 (2011), 92–100

[10] V. K. Andreev, B. B. Bekezhanova, Ustoichivost neizotermicheskikh zhidkostei, Sibirskii federalnyi universitet, Krasnoyarsk, 2010

[11] R. V. Birikh, “O termokapillyarnoi konvektsii v gorizontalnom sloe zhidkosti”, PMTF, 7:3 (1966), 69–72

[12] I. V. Repin, “Statsionarnye techeniya dvukhsloinoi teploprovodnoi zhidkosti v ploskom sloe”, Tr. mezhdunar. konf. “Matematicheskie modeli i metody ikh issledovaniya”, KGU, Krasnoyarsk, 2001, 161–165

[13] V. K. Andreev, Reshenie Birikha uravnenii konvektsii i nekotorye ego obobscheniya, Preprint No 1–10, IVM SO RAN, Krasnoyarsk, 2010, 68 pp.

[14] V. K. Andreev, “Malye vozmuscheniya termokapillyarnogo techeniya zhidkosti s poverkhnostyu razdela”, Tr. sem. “Matematicheskoe modelirovanie v mekhanike”, IVM SO RAN, Krasnoyarsk, 1997, 27–40; Деп. ВИНИТИ 12.02.97, No 446-1397

[15] V. K. Andreev, V. E. Zakhvataev, E. A. Ryabitskii, Termokapillyarnaya neustoichivost, Nauka, Novosibirsk, 2000 | MR

[16] S. K. Godunov, “O chislennom reshenii kraevykh zadach dlya sistem lineinykh obyknovennykh differentsialnykh uravnenii”, Uspekhi mat. nauk, 16:3 (1961), 171–174 | MR | Zbl