Geodesic
On the problem of shear flow stability with respect to long-wave perturbations
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 50-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

To find secondary flow branching to the steady flow it is necessary to consider linear spectral problem and linear adjoint problem. Long-wave asymptotics of linear adjoint problem in two-dimensional case is under consideration. We assume the periodicity with spatial variables when one of the periods tends to infinity. Recurrence formulas are obtained for the $k$th term of the velocity and pressure asymptotics. If the deviation of the velocity from its period-average value is an odd function of spatial variable, the velocity coefficients are odd for odd $k$ and even for even $k$. The relations between coefficients of linear adjoint problem and linear spectral problem are obtained. 
@article{VMJ_2016_18_4_a5,
     author = {S. V. Revina},
     title = {On the problem of shear flow stability with respect to long-wave perturbations},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {50--60},
     year = {2016},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a5/}
}
TY  - JOUR
AU  - S. V. Revina
TI  - On the problem of shear flow stability with respect to long-wave perturbations
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 50
EP  - 60
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a5/
LA  - ru
ID  - VMJ_2016_18_4_a5
ER  - 
%0 Journal Article
%A S. V. Revina
%T On the problem of shear flow stability with respect to long-wave perturbations
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 50-60
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a5/
%G ru
%F VMJ_2016_18_4_a5
S. V. Revina. On the problem of shear flow stability with respect to long-wave perturbations. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 50-60. http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a5/

[1] Yudovich V. I., “Vozniknovenie avtokolebanii v zhidkosti”, Prikl. mat. i mekh., 35:4 (1971), 638–655 | Zbl

[2] Yudovich V. I., “O neustoichivosti parallelnykh techenii vyazkoi neszhimaemoi zhidkosti otnositelno prostranstvenno-periodicheskikh vozmuschenii”, Chislennye metody resheniya zadach mat. fiziki, Nauka, M., 1966, 242–249

[3] Melekhov A. P., Revina S. V., “Vozniknovenie avtokolebanii pri potere ustoichivosti prostranstvenno-periodicheskikh dvumernykh techenii vyazkoi zhidkosti otnositelno dlinnovolnovykh vozmuschenii”, Izv. RAN. MZhG, 2008, no. 2, 41–56

[4] Revina S. V., “Rekurrentnye formuly dlinnovolnovoi asimptotiki zadachi ustoichivosti sdvigovykh techenii”, Zhurn. vychisl. mat. i mat. fiz., 53:8 (2013), 1387–1401 | DOI | Zbl

[5] Revina S. V., Lineinaya sopryazhennaya k zadache ustoichivosti dvumernykh sdvigovykh techenii vyazkoi zhidkosti s nenulevym srednim, Dep. v VINITI 11.08.14, No 228-V2014, M., 2014, 47 pp.