Geodesic
Macroparameters of three-dimensional flows in free shear turbulence
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1126-1139 
O. M. Belotserkovskiǐ; S. V. Fortova. Macroparameters of three-dimensional flows in free shear turbulence. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1126-1139. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a11/
@article{ZVMMF_2010_50_6_a11,
     author = {O. M. Belotserkovskiǐ and S. V. Fortova},
     title = {Macroparameters of three-dimensional flows in free shear turbulence},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1126--1139},
     year = {2010},
     volume = {50},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a11/}
}
TY  - JOUR
AU  - O. M. Belotserkovskiǐ
AU  - S. V. Fortova
TI  - Macroparameters of three-dimensional flows in free shear turbulence
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1126
EP  - 1139
VL  - 50
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a11/
LA  - ru
ID  - ZVMMF_2010_50_6_a11
ER  - 
%0 Journal Article
%A O. M. Belotserkovskiǐ
%A S. V. Fortova
%T Macroparameters of three-dimensional flows in free shear turbulence
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1126-1139
%V 50
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a11/
%G ru
%F ZVMMF_2010_50_6_a11

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

The initial stage of the onset of turbulence in a three-dimensional compressible inviscid shear flow is studied. An initial deterministic velocity perturbation in the form of one or several Fourier modes leads to the development of a cascade of instabilities, which is numerically simulated. The influence exerted on the formation of the cascade of instabilities and the transition to turbulence by the size of the computational domain, the shear layer width, and the initial conditions is analyzed. It is shown that the mechanism of turbulence onset is essentially three-dimensional. The influence of various flow parameters and initial conditions on the formation of the turbulence cascade is studied numerically.

[1] Belotserkovskii O. M., Karman's lecture, von Karman institute for fluid dynamics, 1978

[2] Belotserkovskii O. M., Turbulence and instabilities, MZpress Publ., M., 2003

[3] Belotserkovskii O. M., Oparin A. M., Chechetkin V. M., Turbulentnost: novye podkhody, Nauka, M., 2003

[4] Belotserkovskii O. M., Oparin A. M., Chechetkin V. M., “Fizicheskie protsessy razvitiya sdvigovoi turbulentnosti”, Zh. eksperim. i teor. fiz., 126:3(9) (2004), 577–584

[5] Thomson W., “On the propagation of laminar motion through a turbulently moving inviscid liquid”, Philos. Mag., 4:47 (1887), 342

[6] Lord Rayleigh F. R. S., “On the stability, or instability, of certain fluid motions”, Proc. London Soc., S1–11 (1880), 57–72

[7] Richardson L. F., “Atmospheric diffusion shown on a distance-neighbour graph”, Proc. Roy. Soc. London, 110 (1926), 709–737 | DOI

[8] Kolmogorov A. N., “Lokalnaya struktura turbulentnosti v neszhimaemoi vyazkoi zhidkosti pri ochen bolshikh chislakh Reinoldsa”, Dokl. AN SSSR, 30:4 (1940), 476–481

[9] Troshkin O. V., Nontraditional methods in mathematical hydrodynamics, 144, Amer. Math. Soc., Providence, RI, 1995 | MR | Zbl

[10] Belotserkovskii O. M., Oparin A. M., Chislennyi eksperiment: ot poryadka k khaosu, Nauka, M., 2000

[11] Belotserkovskii O. M., Chechetkin V. M., Fortova S. V., Oparin A. M., “The turbulence of free shear flows”, Hot Points in Astrophysics and Cosmology, Proc. Internat. Workshop, Dubna, 2005, 191–209

[12] Belotserkovskii O., Fortova S., Oparin A. et al., “The turbulence in free shear flows and in accretion disks”, Investigations Hydrodynamical Instability and Turbulence in Fundamental and Technol. Problems by Means of Math. Modeling with Supercomput., Nagoya, Japan, 2007, 229–241

[13] Meshkov E. E., “Neustoichivost granitsy razdela dvukh gazov, uskoryaemoi udarnoi volnoi”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 5 (1969), 151–158

[14] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[15] Yanase S., Kaga Y., “Zero-absolute-vorticity-state of rotating flows between plates”, Japan-Russia Seminar on Turbulence and Instabilities (2003, Sept. 29–30, Tokyo), 2003

[16] Hoffman J., Johnson C., On transition to turbulence in shear flow, Preprint. Roy. Inst. Technol. Kunliga Tekniska Hogskolan, 2002 | MR

[17] Fortova S. V., “The cascade mechanism in free shear flows”, 24 Internat. Conf. Interaction of Intense Energy Fluxes with Matter, Poster Session (March 1–6, Elbrus, Russia, 2009)

[18] Fortova S. V., “On vortex cascades in shear flow instabilities”, Turbulent Mixing and Beyond, 2nd Internat. Conf. and Advanced School (2009, Trieste, Italy), 2009

[19] Belotserkovskii O. M., Oparin A. M., Troshkin O. V., Chechetkin V. M., “Constructive modeling of structural turbulence: computational experiment”, Phys. Scripta, 132 (2008)

[20] Oparin A. M., “Chislennoe modelirovanie problem, svyazannykh s intensivnym razvitiem gidrodinamicheskikh neustoichivostei”, Novoe v chisl. modelirovanii: algoritmy, vychisl. eksperiment, rezultat, Nauka, M., 2000, 63–90 | MR

[21] Oparin A. M., “Numerical study of hydrodynamic instabilities”, Comput. Fluid Dynamics J., 10:3, Spec. Issue (2001), 327–332

[22] Belotserkovskii O. M., Kraginskii L. M., Oparin A. M., “Chislennoe modelirovanie prostranstvennykh techenii v stratifitsirovannoi atmosfere, vyzvannykh silnymi krupnomasshtabnymi vozmuscheniyami”, Zh. vychisl. matem. i matem. fiz., 43:11 (2003), 1722–1736 | MR | Zbl

[23] Sakurai A., Takayama K., “Molecular kinetic approach to the problem of compressible turbulence”, Phys. Fluid, 15:5 (1995), 1282–1897 | DOI

[24] Belotserkovskii O. M., Guschin V. A., Konshin V. N., “Metod rasschepleniya dlya issledovaniya techenii stratifitsirovannoi zhidkosti so svobodnoi poverkhnostyu”, Zh. vychisl. matem. i matem. fiz., 27:4 (1987), 594–609 | MR

[25] Betchelor Dzh. K., Teoriya odnorodnoi turbulentnosti, Izd-vo inostr. lit., M., 1955

[26] Kovenya V. M., Yanenko N. N., Metod rasschepleniya v zadachakh gazovoi dinamiki, Nauka, Novosibirsk, 1981 | MR | Zbl

[27] Courant R., Isaacon E., Rees M., “On the solution of nonlinear hyperbolic differential equations by finite differences”, Communs Pure and Appl. Math., 5 (1952), 124–130 | DOI | MR

[28] Roe P. L., “Characteristic-based schemes for the Euler equations”, Ann. Rev. Fluid Mech., 18 (1986), 248–254 | DOI | MR

[29] Harten A., “High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49:2 (1983), 151 | DOI | MR | Zbl

[30] Monin A. S., Etyudy o turbulentnosti, Nauka, M., 1994