@article{ZVMMF_2009_49_4_a15,
author = {O. M. Belotserkovskii and V. V. Denisenko and A. V. Konyukhov and A. M. Oparin and O. V. Troshkin and V. M. Chechetkin},
title = {Numerical stability analysis of the {Taylor{\textendash}Couette} flow in the two-dimensional case},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {754--768},
year = {2009},
volume = {49},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a15/}
}
TY - JOUR AU - O. M. Belotserkovskii AU - V. V. Denisenko AU - A. V. Konyukhov AU - A. M. Oparin AU - O. V. Troshkin AU - V. M. Chechetkin TI - Numerical stability analysis of the Taylor–Couette flow in the two-dimensional case JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2009 SP - 754 EP - 768 VL - 49 IS - 4 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a15/ LA - ru ID - ZVMMF_2009_49_4_a15 ER -
%0 Journal Article %A O. M. Belotserkovskii %A V. V. Denisenko %A A. V. Konyukhov %A A. M. Oparin %A O. V. Troshkin %A V. M. Chechetkin %T Numerical stability analysis of the Taylor–Couette flow in the two-dimensional case %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2009 %P 754-768 %V 49 %N 4 %U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a15/ %G ru %F ZVMMF_2009_49_4_a15
O. M. Belotserkovskii; V. V. Denisenko; A. V. Konyukhov; A. M. Oparin; O. V. Troshkin; V. M. Chechetkin. Numerical stability analysis of the Taylor–Couette flow in the two-dimensional case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 754-768. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a15/
[1] Taylor G., “Stability of a viscous liquid contained between two rotating cylinders”, Philos. Trans. Roy. Soc. London. Ser. A, 223 (1923), 289–343 | DOI | Zbl
[2] Kochin N. E., Kibel I. A., Roze N. V., Teoreticheskaya gidromekhanika, Ch. 2, Fizmatgiz, M., 1963 | Zbl
[3] Belotserkovskii O. M., Oparin A. M., Chechetkin V. M., “Obrazovanie krupnomasshtabnykh struktur v zazore mezhdu vraschayuschimisya tsilindrami (zadacha Releya–Zeldovicha)”, Zh. vychisl. matem. i matem. fiz., 42:11 (2002), 1727–1737 | MR | Zbl
[4] Sun Liang, “General stability criterion for inviscid parallel flow”, European J. Phys., 28:5 (2007), 889–895 | DOI | Zbl
[5] Belotserkovskii O. M., Oparin A. M., Chechetkin V. M., Turbulentnost: novye podkhody, Nauka, M., 2003
[6] Landau L. D., Lifshits E. M., Teoreticheskaya fizika. T. 6. Gidrodinamika, Izd. 3-e, Nauka, M., 1986 | MR
[7] Lord Rayleigh F. R. S., “On the stabiligy, or instability, of certain fluid motions”, Proc. London Soc., 11 (1880), 57–72
[8] Lord Rayleigh F. R. S., “On the dynamics of revolving fluids”, Proc. London Soc. A, 93 (1916), 148–154
[9] Reynolds O., “On the dynamical theory of incompressible viscous fluids and the determination of the criterion”, Philos. Trans. Roy. Soc. London. Ser. A, 186 (1895), 123–164 | DOI
[10] Lin Tszyao-tszyao, Teoriya gidrodinamicheskoi ustoichivosti, Izd-vo inostr. lit., M., 1958
[11] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR
[12] Yudovin V. I., “Ob ustoichivosti statsionarnykh techenii vyazkoi neszhimaemoi zhidkosti”, Dokl. AN SSSR, 5 (1965), 1037–1040
[13] Ivanilov Yu. P., Yakovlev G. N., “O bifurkatsii techeniya zhidkosti mezhdu vraschayuschimisya tsilindrami”, Prikl. matem. i mekhan., 30 (1966), 910–916 | MR | Zbl
[14] Ruelle D., Takens F., “On the nature of turbulence”, Communs. Math. Phys., 20 (1971), 167–192 | DOI | MR | Zbl
[15] Dzhozef D., Ustoichivost dvizhenii zhidkosti, Mir, M., 1981
[16] Zubarev D. H., Morozov V. G., Troshkin O. V., “Bifurkatsionnaya model turbulentnogo techeniya v kanale”, Dokl. AN SSSR, 290:2 (1986), 313–317 | MR | Zbl
[17] Oparina E. I., Troshkin O. V., “Ustoichivost techeniya Kolmogorova v kanale s tverdymi stenkami”, Dokl. RAN, 398:4 (2004), 487–491 | MR
[18] Fridman A. A., Opyt gidromekhaniki szhimaemoi zhidkosti, ONTI, M., 1934
[19] Heimholtz H. L. F., Über discontinuierlich Flussigkeitsbewegungen, Monatsberichte königl, Akad. Wiss., Berlin, 1868
[20] Kelvin (W. Thomson), Mathematical and physical papers, V. 4, Cambridge Univ. Press, 1910 | Zbl
[21] Richtmyer R. D., “Taylor instability in a shock acceleration of compressible fluids”, Communs Pure and Appl. Math., 13:2 (1960), 297–319 | DOI | MR
[22] Meshkov E. E., “Neustoichivost granitsy razdela dvukh gazov, uskoryaemoi udarnoi volnoi”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1969, no. 5, 151–158
[23] Taylor G. I. I., “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I”, Pros. Roy. Soc. London. Ser. A, 201:1065 (1950), 192–196 | DOI | MR | Zbl
[24] Bénard H., “Les tourbillons cellulaires dans une nappe liquide”, Rev. générale d es Sci. pures et appl., 11 (1900), 1261–1309
[25] Bénard H., “Les tourbillons cellulaires une nappe liquide transportant de la chaleur par convection en regime permanent”, Ann. Chim. Phys., 23 (1901), 62–144 | Zbl
[26] Arnold V., “Sur la topologie des ecoulement stationnaires des fluides parfaites”, C. R. Acad. Sci., 261:1 (1965), 17–20 | MR
[27] Anrold V., “Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits”, Ann. Inst. Fourier, 16 (1966), 319–361 | MR
[28] Meshalkin L. D., Sinai Ya. G., “Issledovanie ustoichivosti statsionarnogo resheniya odnoi sistemy uravnenii ploskogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Prikl. matem. i mekhan., 25:6 (1961), 1140–1143 | Zbl
[29] Troshkin O. V., Nontraditional methods in mathematical hydrodynamics, Amer. Math. Soc., Providence, RI, 1995 | MR | Zbl
[30] Troshkin O. B., “O topologicheskom analize struktury gidrodinamicheskikh techenii”, Uspekhi matem. nauk, 43:4(262), 129–158 | MR | Zbl
[31] Belotserkovskii O. M., “Computational experiment: direct numerical simulation of complex gas-dynamics flows on the basis of Euler, Navier–Stokes, and Boltzmann models”, Numerical Methods in Fluid Dynamics, Series in Thermal and Fluids Engineering, eds. H. J. Wirz and J. J. Smolderen, Hemisphere, Washington, 1978, 339–387
[32] Belotserkovskii O. M., “Pryamoe chislennoe modelirovanie svobodnoi razvitoi turbulentnosti”, Zh. vychisl. matem. i matem. fiz., 25:12 (1985), 1856–1882 | MR
[33] Belotserkovskii O. M., Turbulence and instabilities, MZpress Pubs, M., 2003
[34] Belotserkovskii O. M., Oparin A. M., Chechetkin V. M., Turbulence: new approaches, CISP CBI 6AZ, Cambridge, 2005
[35] Belotserkovskii O., Fortova S., Oparin A. et al., “The turbulence in free shear flows and in accretion disks”, Investigation of hydrodynamic instability and turbulence in fundamental and technological problems by means of mathematical modeling with supercomputers, Nagoya Univ., Nagoya, Japan, 2005, 229–241
[36] Ranque G., “Experiments on expansion in a vortex with simultaneous exhaust of hot and air”, J. Phys. et de la Radium, 4:6 (1933), 1125–1130
[37] Hilsch R., “The use of the expansion of gases in a centrifugal field as cooling process”, Rev. Sci. Instruments, 18:2 (1947), 108–1113 | DOI
[38] Dirak P. A. M., Sobranie nauchnykh trudov, Tom 4, Fizmatlit, M., 2005
[39] Aisen E. M., Borisevich V. D., Levin E. V., “Modelirovanie techeniya i diffuzii v gazovoi tsentrifuge dlya razdeleniya mnogokomponentnykh izotopnykh smesei”, Matem. modelirovanie, 9:4 (1997), 27–38 | Zbl
[40] Saffman P. G., Taylor G. I., “The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid”, Proc. Roy. Soc. London. Ser. A, 245 (1958), 312–329 | DOI | MR | Zbl
[41] Belotserkovskaya M. S., Chislennoe modelirovanie protsessov filtratsii s ispolzovaniem metoda vlozhennykh setok, Dis. $\dots$ kand. fiz.-matem. nauk, MGU, M., 2007