Geodesic
Numerical simulation of Rayleigh–Taylor instability in inviscid and viscous media
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 876-885 
A. N. Doludenko; S. V. Fortova. Numerical simulation of Rayleigh–Taylor instability in inviscid and viscous media. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 876-885. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a12/
@article{ZVMMF_2015_55_5_a12,
     author = {A. N. Doludenko and S. V. Fortova},
     title = {Numerical simulation of {Rayleigh{\textendash}Taylor} instability in inviscid and viscous media},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {876--885},
     year = {2015},
     volume = {55},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a12/}
}
TY  - JOUR
AU  - A. N. Doludenko
AU  - S. V. Fortova
TI  - Numerical simulation of Rayleigh–Taylor instability in inviscid and viscous media
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 876
EP  - 885
VL  - 55
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a12/
LA  - ru
ID  - ZVMMF_2015_55_5_a12
ER  - 
%0 Journal Article
%A A. N. Doludenko
%A S. V. Fortova
%T Numerical simulation of Rayleigh–Taylor instability in inviscid and viscous media
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 876-885
%V 55
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a12/
%G ru
%F ZVMMF_2015_55_5_a12

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

The Rayleigh–Taylor instability in viscous and inviscid compressible media is analyzed by applying the numerical simulation of the Euler and Navier–Stokes equations. It is shown that the development of hydrodynamic instabilities leads to the formation of an eddy cascade, which, after the onset of turbulence in the flow, corresponds to an eddy cascade developing in the energy and inertial ranges. The results reveal that the developing flows and the parameters under study are identical for both models.

[1] Richardson L. F., “The supply of energy from and to atmospheric eddies”, Proc. Roy. Soc. London A, 97 (1920), 354–373

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

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

[4] Ievlev V. M., Chislennoe modelirovanie turbulentnykh techenii, Nauka, M., 1990 | MR

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

[6] 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 | Zbl

[7] Layzer D., “On the Instability of Superposed Fluids in a Gravitational Field”, Astrophys. J., 122 (1955), 1–12 | MR

[8] Bell G. I., Taylor instability on cylinders and spheres in the small amplitude approximation, Rep. La-1321, Los Alamos National Laboratory, 1951

[9] Plesse M. S., “On the stability of fluid flows with spherical symmetry”, J. Appl. Phys., 25 (1954), 96–98 | MR | Zbl

[10] Mikaelian K. O., “Effect of viscosity on Rayleigh–Taylor and Richtmyer–Meshkov instabilities”, Phys. Rev. N-E, 47 (1993), 375–383

[11] Inogamov N. A., Demyanov A. Yu., Son E. E., Gidrodinamika peremeshivaniya, Izd-vo MFTI, M., 1999

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

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

[14] 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 | Zbl

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

[16] 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

[17] Fortova S. V., “Chislennoe modelirovanie trekhmernogo techeniya Kolmogorova dlya sdvigovogo sloya”, Zh. vychisl. i matem. i matem. fiz., 53:3 (2013), 433–441 | Zbl

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

[19] Inogamov N., “Statistics of long-wavelength fluctuations and the expansion rate of Richtmyer–Meshkov turbulence zone”, JETP Lett., 75:11 (2010), 547–551

[20] Belotserkovskii O. M., Davydov Yu. M., Demyanov A. Yu., “Vzaimodeistvie mod vozmuschenii pri neustoichivosti Releya–Teilora”, Dokl. AN SSSR, 288 (1986), 1071