Geodesic
2-dimensional streamwise periodical solutions of Navier–Stokes equations for plane channel
Matematičeskoe modelirovanie, Tome 19 (2007) no. 6, pp. 118-128 
S. G. Ponomarev; M. I. Stoynov. 2-dimensional streamwise periodical solutions of Navier–Stokes equations for plane channel. Matematičeskoe modelirovanie, Tome 19 (2007) no. 6, pp. 118-128. http://geodesic.mathdoc.fr/item/MM_2007_19_6_a9/
@article{MM_2007_19_6_a9,
     author = {S. G. Ponomarev and M. I. Stoynov},
     title = {2-dimensional streamwise periodical solutions of {Navier{\textendash}Stokes} equations for plane channel},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {118--128},
     year = {2007},
     volume = {19},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_6_a9/}
}
TY  - JOUR
AU  - S. G. Ponomarev
AU  - M. I. Stoynov
TI  - 2-dimensional streamwise periodical solutions of Navier–Stokes equations for plane channel
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 118
EP  - 128
VL  - 19
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_6_a9/
LA  - ru
ID  - MM_2007_19_6_a9
ER  - 
%0 Journal Article
%A S. G. Ponomarev
%A M. I. Stoynov
%T 2-dimensional streamwise periodical solutions of Navier–Stokes equations for plane channel
%J Matematičeskoe modelirovanie
%D 2007
%P 118-128
%V 19
%N 6
%U http://geodesic.mathdoc.fr/item/MM_2007_19_6_a9/
%G ru
%F MM_2007_19_6_a9

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

Results of computer simulations are given for nonstationary viscous incompressible fluid flows in an infinite plane channel. Two-dimensional streamwise periodic solutions of the Navier–Stokes equations are investigated. It is shown that if the wave number $\alpha_0$ tends to zero the integral characteristics of the flows are no longer dependent on $\alpha_0$ and determined by the Reynolds number only. Nonuniqueness of secondary longwave flows is established. Regions of existence for the secondary flows with different $\alpha_0$ are studied.

[1] Temam R., Uravnenie Nave–Stoksa: teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[2] Goldshtik M. A., Shtern V. N., Gidrodinamicheskaya ustoichivost i turbulentnost, Nauka, Novosibirsk, 1977

[3] Ponomarev S. G., Rozhdestvenskii B. L., Stoinov M. I., Mat. Modelirovanie, 6:5 (1994), 3–14 | MR | Zbl

[4] Rozhdestvenskii B. L., Simakin I. N., Zh. Vychisl. matem. i matem. Fiz., 25:1 (1985), 96–121 | MR | Zbl

[5] Rozhdestvenskii B.L., Stoinov M.I., Preprint 119, IP Matem. im. M. V. Keldysha AN SSSR, M., 1987 | MR

[6] Kim J., Moin P., Moser R., J. Fluid Mech., 177 (1987), 133–166 | DOI | Zbl

[7] Ponomarev S. G., Priimak V. G., Rozhdestvenskii B. L., Zh. Vychisl. matem. i matem.Fiz., 28:9 (1988), 1354–1366 | MR

[8] Herbert T., AIAA J., 18:3 (1980), 243–248 | DOI | MR | Zbl

[9] Jimenez J., “Transition to turbulence in two-dimensional Poiseulle flow”, J. Fluid Mech., 218 (1990), 265–297 | DOI

[10] Priymak V. G., Miyazaki T., “Direct numerical simulation of equilibrium spatially localized structures in pipe flow”, Phys. Fluids, 16 (2004), 4221–4234 | DOI