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Uspekhi Mat. Nauk, 1983, Volume 38, Issue 4(232), Pages 101–111 (Mi umn2946)  

This article is cited in 37 scientific papers (total in 37 papers)

Kolmogorov flow and laboratory simulation of it

A. M. Obukhov

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English version:
Russian Mathematical Surveys, 1983, 38:4, 113–126

Bibliographic databases:

UDC: 532.51+54
MSC: 76F10, 76F55, 76E30, 76F05
Received: 26.04.1983

Citation: A. M. Obukhov, “Kolmogorov flow and laboratory simulation of it”, Uspekhi Mat. Nauk, 38:4(232) (1983), 101–111; Russian Math. Surveys, 38:4 (1983), 113–126

Citation in format AMSBIB
\by A.~M.~Obukhov
\paper Kolmogorov flow and laboratory simulation of~it
\jour Uspekhi Mat. Nauk
\yr 1983
\vol 38
\issue 4(232)
\pages 101--111
\jour Russian Math. Surveys
\yr 1983
\vol 38
\issue 4
\pages 113--126

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    This publication is cited in the following articles:
    1. G. Sivashinsky, V. Yakhot, “Negative viscosity effect in large-scale flows”, Phys Fluids, 28:4 (1985), 1040  crossref  zmath  adsnasa  isi
    2. Gregory I. Sivashinsky, “Weak turbulence in periodic flows”, Physica D: Nonlinear Phenomena, 17:2 (1985), 243  crossref
    3. L. A. Belousov, “The asymptotic behaviour for large $t$ of the Fourier coefficients of solutions of the Meshalkin problem”, Russian Math. Surveys, 41:3 (1986), 199–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Zhen Su She, “Metastability and vortex pairing in the kolmogorov flow”, Physics Letters A, 124:3 (1987), 161  crossref
    5. Basil Nicolaenko (Nichols), “Large scale spatial structures in two-dimensional turbulent flows”, Nuclear Physics B - Proceedings Supplements, 2 (1987), 453  crossref
    6. Roland Grappin, Jacques Leorat, Pasquale Londrillo, “Onset and development of turbulence in two-dimensional periodic shear flows”, J Fluid Mech, 195:-1 (1988), 239  crossref  isi
    7. F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin, “Stability and vortex structures of quasi-two-dimensional shear flows”, Uspekhi fizicheskikh nauk, 160:7 (1990), 1  crossref
    8. Roland Grappin, Jacques Léorat, “Lyapunov exponents and the dimension of periodic incompressible Navier—Stokes flows: numerical measurements”, J Fluid Mech, 222:-1 (1991), 61  crossref  mathscinet  zmath  isi
    9. M. A. Brutyan, P. L. Krapivsky, “Stability of periodic space flows of a viscous fluid”, U.S.S.R. Comput. Math. Math. Phys., 31:4 (1991), 111–114  mathnet  mathscinet  zmath  isi
    10. M.A. Brutyan, P.L. Krapivsky, “Stability of periodic unidirectional flows in three dimensions”, Physics Letters A, 152:3-4 (1991), 211  crossref  elib
    11. M.A. Brutyan, P.L. Krapivsky, “On the stability of periodic unidirectional flows of micropolar fluid”, International Journal of Engineering Science, 30:3 (1992), 401  crossref
    12. Weinan E, Chi-Wang Shu, “Effective equations and the inverse cascade theory for Kolmogorov flows”, Phys Fluids A, 5:4 (1993), 998  crossref  mathscinet  zmath  adsnasa  isi
    13. H. Okamoto, M. Shōji, “Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori”, Japan J Indust Appl Math, 10:2 (1993), 191  crossref  mathscinet
    14. Alexander L. Frenkel, Xiaojing Zhang, “Large-Scale Instability of Generalized Oscillating Kolmogorov Flows”, SIAM J Appl Math, 58:2 (1998), 540  crossref  mathscinet  zmath  isi
    15. M. Malek Mansour, C. Van den Broeck, I Bena, F Baras, “Spurious diffusion in particle simulations of the Kolmogorov flow”, Europhys Lett, 47:1 (1999), 8  crossref  adsnasa  isi
    16. I. Bena, M. Malek Mansour, F. Baras, “Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime”, Phys Rev E, 59:5 (1999), 5503  crossref  mathscinet  adsnasa  isi
    17. I. Bena, F. Baras, M. Malek Mansour, “Hydrodynamic fluctuations in the Kolmogorov flow: Nonlinear regime”, Phys Rev E, 62:5 (2000), 6560  crossref  adsnasa  isi
    18. Zhi-Min Chen, W.G. Price, “Onset of Chaotic Kolmogorov Flows Resulting from Interacting Oscillatory Modes”, Comm Math Phys, 256:3 (2005), 737  crossref  mathscinet  zmath  adsnasa  isi
    19. G. V. Sandrakov, “On some properties of solutions of Navier-Stokes equations with oscillating data”, J. Math. Sci. (N. Y.), 143:4 (2007), 3377–3385  mathnet  crossref  mathscinet
    20. G. Gambino, M.C. Lombardo, M. Sammartino, “Adaptive control of a seven mode truncation of the Kolmogorov flow with drag”, Chaos, Solitons & Fractals, 41:1 (2009), 47  crossref
    21. Sun-Chul Kim, Hisashi Okamoto, “Vortices of large scale appearing in the 2D stationary Navier–Stokes equations at large Reynolds numbers”, Japan J Indust Appl Math, 2010  crossref
    22. I. E. Sarris, D. G. E. Grigoriadis, N. S. Vlachos, “Laminar Free Convection in a Square Enclosure Driven by the Lorentz Force”, Num. Heat Transfer, Part A: Applications, 58:12 (2010), 923  crossref
    23. Douglas H. Kelley, Nicholas T. Ouellette, “Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment”, Am. J. Phys, 79:3 (2011), 267  crossref
    24. Stepanyants Yu.A., Yakubovich E.I., “Skalyarnoe opisanie trekhmernykh vikhrevykh techenii neszhimaemoi zhidkosti”, Doklady akademii nauk, 436:6 (2011), 764–767  elib
    25. Batchaev A.M., “Ploskoe techenie neszhimaemoi zhidkosti pod deistviem periodicheskoi sily i ego geofizicheskoe prilozhenie”, Izvestiya rossiiskoi akademii nauk. fizika atmosfery i okeana, 47:4 (2011), 552–561  elib
    26. O. N. Shablovskii, “Trigonometricheskii profil skorosti sdvigovogo techeniya vyazkoi zhidkosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 77–82  mathnet  elib
    27. Marco Martins Afonso, Andrea Mazzino, Paolo Muratore-Ginanneschi, “Eddy diffusivities of inertial particles under gravity”, J. Fluid Mech, 2012, 1  crossref
    28. Batchaev A.M., “Laboratornoe modelirovanie techeniya kolmogorova na sfericheskoi poverkhnosti”, Izvestiya rossiiskoi akademii nauk. fizika atmosfery i okeana, 48:6 (2012), 733–733  elib
    29. S. V. Fortova, “Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer”, Comput. Math. Math. Phys., 53:3 (2013), 311–319  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. Balachandra Suri, Jeffrey Tithof, Radford Mitchell, R.O.. Grigoriev, M.F.. Schatz, “Velocity profile in a two-layer Kolmogorov-like flow”, Phys. Fluids, 26:5 (2014), 053601  crossref
    31. Dan Lucas, Rich Kerswell, “Spatiotemporal dynamics in two-dimensional Kolmogorov flow over large domains”, J. Fluid Mech, 750 (2014), 518  crossref
    32. Akanksha Gupta, R. Ganesh, Ashwin Joy, “Kolmogorov flow in two dimensional strongly coupled dusty plasma”, Phys. Plasmas, 21:7 (2014), 073707  crossref
    33. N. M. Zhabborov, Kh. Kh. Imomnazarov, P. V. Korobov, “Three-Dimensional Vortex Flows of Incompressible Media in the Case of the Constant Volume Saturation Substances”, J. Math. Sci., 211:6 (2015), 760–766  mathnet  crossref
    34. Eiichi Sasaki, Shin-ichi Takehiro, Michio Yamada, “Bifurcation structure of two-dimensional viscous zonal flows on a rotating sphere”, J. Fluid Mech, 774 (2015), 224  crossref
    35. Sun-Chul Kim, Hisashi Okamoto, “Unimodal patterns appearing in the Kolmogorov flows at large Reynolds numbers”, Nonlinearity, 28:9 (2015), 3219  crossref
    36. S. V. Revina, “Stability of the Kolmogorov flow and its modifications”, Comput. Math. Math. Phys., 57:6 (2017), 995–1012  mathnet  crossref  crossref  mathscinet  isi  elib
    37. O. V. Kirichenko, S. V. Revina, “On the stability of two-dimensional flows close to the shear”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:3 (2019), 28–41  mathnet  crossref  elib
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