Geodesic
Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 433-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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Numerical simulation is used to study the Kolmogorov flow in a shear layer of a compressible inviscid medium. A periodic permanent force applied to the flow gives rise to a vortex cascade of instabilities. The influence exerted by the size of the computational domain, the initial conditions, and the amplitude of the force on the formation of an instability cascade and the transition to turbulence is studied. It is shown that the mechanism of the onset of turbulence has an essentially three-dimensional nature. For the turbulent flows computed, the classical Kolmogorov $-5/3$ power law holds in the inertial range. 
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S. V. Fortova. Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 433-441. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a10/

[1] Kolmogorov A. N., “Lokalnaya struktura turbulentnosti v neszhimaemoi zhidkosti pri ochen bolshikh chislakh Reinoldsa”, Dokl. AN SSSR, 30:4 (1941), 299–303

[2] Arnold V. I., Meshalkin L. D., “Seminar A. N. Kolmogorova po izbrannym voprosam analiza (1958–1959)”, Uspekhi matem. nauk, 15:1 (1960), 247–250

[3] Meshalkin L. D., Sinai Ya. G., “Issledovanie ustoichivosti statsionarnogo resheniya odnoi sistemy uravnenii ploskogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Zh. prikl. matem. i mekhan., 25:6 (1961), 1140–1143 | Zbl

[4] Obukhov A. M., “O raspredelenii energii v spektre turbulentnogo potoka”, Izv. AN SSSR. Geogr. i geofiz., 5:4 (1941), 453–466

[5] Belotserkovskii S. O., Mirabel A. P., Chusov M. A., “O postroenii zakriticheskogo rezhima dlya ploskogo periodicheskogo techeniya”, Izv. AN SSSR. Fiz. atmosf. i okeana, 14:1 (1978), 11–20

[6] Yudovich V. I., “Ob avtokolebaniyakh, voznikayuschikh pri potere ustoichivosti parallelnykh techenii vyazkoi zhidkosti otnositelno dlinnovolnovykh periodicheskikh vozmuschenii”, Izv. AN SSSR. Mekhan. zhidk. i gaza, 1973, no. 1, 32–35

[7] Bondarenko N. F., Gak M. Z., Dolzhanskii F. V., “Laboratornaya i teoreticheskie modeli ploskogo periodicheskogo techeniya”, Izv. AN SSSR. Fiz. atmosf. i okeana, 15:10 (1979), 1017–1026 | MR

[8] Belotserkovskii O. M., Oparin A. M., Chislennyi eksperiment: ot poryadka k khaosu, Nauka, M., 2000, 106–130

[9] Landau L. D., Lifshits E. M., Mekhanika sploshnykh sred, Gostekhteorizdat, M., 1953

[10] Belotserkovskii O. M., Oparin A. M., Chechetkin V. M., Turbulentnost: novye podkhody, Nauka, M., 2002

[11] Obukhov A. M., “Techenie Kolmogorova i ego laboratornoe modelirovanie”, Uspekhi matem. nauk, 38:4(232) (1983), 101–111 | MR

[12] Monin A. S., Yaglom A. M., Statisticheskaya gidromekhanika, Nauka, M., 1967

[13] Chepmen D. R., “Vychislitelnaya gidrodinamika i perspektivy ee razvitiya: draidenovskaya lektsiya”, Raketnaya tekhnika i kosmonavtika, 18:2 (1980), 3–32

[14] Faber T. E., Gidroaerodinamika, Postmarket, M., 2001

[15] Kucherenko Yu. A. i dr., “Izmerenie spektralnykh kharakteristik zony turbulentnogo peremeshivaniya”, Prikl. mekhan. i tekhn. fiz., 51:3 (2010), 3–13 | MR

[16] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1978 | MR

[17] Hoffman J., Johnson C., On transition to turbulence in shear flow, Prepr. 2000_4, Finit Element Center, Chalmers, 2002

[18] Rogers M. M., Moser R. D., “The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup”, J. Fluid Mech., 243 (1992), 183–226 | DOI | Zbl

[19] Moser R. D., Rogers M. M., “The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence”, J. Fluid Mech., 247 (1993), 275–320 | DOI | Zbl

[20] 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. Intern. Workshop (Dubna, 2005), 191–209

[21] Belotserkovskii O. M., Fortova S. V., “Makroparametry prostranstvennykh techenii v svobodnoi sdvigovoi turbulentnosti”, Zh. vychisl. matem. i matem. fiz., 50:6 (2010), 1126–1139 | MR | Zbl

[22] 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

[23] Troshkin O. V., “Dissipativnyi volchok na slabokompaktnoi algebre Li i ustoichivost osnovnykh techenii v ploskom kanale”, Dokl. AN SSSR. Mekhan., 442:2 (2012), 1–6 | MR

[24] Inogamov N., “Statistics of long-wavelength fluctuations and the expansion rate of Richtmyer–Meshkov turbulence zone”, Jetp letters, 75:11, 547–551 | DOI