메뉴 건너뛰기




Volumn 22, Issue 4, 2012, Pages

Periodic orbits near onset of chaos in plane Couette flow

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84871896072     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4757227     Document Type: Article
Times cited : (138)

References (50)
  • 1
    • 35949023610 scopus 로고
    • Roads to turbulence in dissipative dynamical systems
    • 10.1103/RevModPhys.53.643
    • Eckmann J. Roads to turbulence in dissipative dynamical systems. Rev. Mod. Phys. 1981, 53:643-654. 10.1103/RevModPhys.53.643.
    • (1981) Rev. Mod. Phys. , vol.53 , pp. 643-654
    • Eckmann, J.1
  • 2
    • 35949021570 scopus 로고
    • Strange attractors and chaotic motions of dynamical systems
    • 10.1103/RevModPhys.53.655
    • Ott E. Strange attractors and chaotic motions of dynamical systems. Rev. Mod. Phys. 1981, 53:655-671. 10.1103/RevModPhys.53.655.
    • (1981) Rev. Mod. Phys. , vol.53 , pp. 655-671
    • Ott, E.1
  • 3
    • 33846046266 scopus 로고    scopus 로고
    • Turbulence transition in pipe flow
    • 10.1146/annurev.fluid.39.050905.110308
    • Eckhardt B. Schneider T.M. Hof B. Westerweel J. Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 2007, 39:447-468. 10.1146/annurev.fluid.39.050905.110308.
    • (2007) Annu. Rev. Fluid Mech. , vol.39 , pp. 447-468
    • Eckhardt, B.1    Schneider, T.M.2    Hof, B.3    Westerweel, J.4
  • 4
    • 38849090768 scopus 로고    scopus 로고
    • Turbulence transition in pipe flow: Some open questions
    • 10.1088/0951-7715/21/1/T01
    • Eckhardt B. Turbulence transition in pipe flow: Some open questions. Nonlinearity 2008, 21:T1. 10.1088/0951-7715/21/1/T01.
    • (2008) Nonlinearity , vol.21
    • Eckhardt, B.1
  • 5
    • 0001397592 scopus 로고
    • Periodic orbits and classical quantization conditions
    • 10.1063/1.1665596
    • Gutzwiller M.C. Periodic orbits and classical quantization conditions. J. Math. Phys. 1971, 12(3):343. 10.1063/1.1665596.
    • (1971) J. Math. Phys. , vol.12 , Issue.3 , pp. 343
    • Gutzwiller, M.C.1
  • 7
    • 0000835319 scopus 로고
    • Periodic orbit expansions for classical smooth flows
    • 10.1088/0305-4470/24/5/005
    • Cvitanović P. Eckhardt B. Periodic orbit expansions for classical smooth flows. J. Phys. A 1991, 24:L237. 10.1088/0305-4470/24/5/005.
    • (1991) J. Phys. A , vol.24
    • Cvitanović, P.1    Eckhardt, B.2
  • 8
    • 0022677808 scopus 로고
    • Flow regimes in a circular Couette system with independently rotating cylinders
    • 10.1017/S0022112086002513
    • Andereck C.D. Liu S.S. Swinney H.L. Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 1986, 164:155-183. 10.1017/S0022112086002513.
    • (1986) J. Fluid Mech. , vol.164 , pp. 155-183
    • Andereck, C.D.1    Liu, S.S.2    Swinney, H.L.3
  • 10
    • 0018505940 scopus 로고
    • Rayleigh-Bénard experiment in liquid helium; frequency locking and the onset of turbulence
    • 10.1051/jphyslet:019790040016041900
    • Maurer J. Libchaber A. Rayleigh-Bénard experiment in liquid helium; frequency locking and the onset of turbulence. J. Phys. Lett. 1979, 40:419-423. 10.1051/jphyslet:019790040016041900.
    • (1979) J. Phys. Lett. , vol.40 , pp. 419-423
    • Maurer, J.1    Libchaber, A.2
  • 11
    • 0008978763 scopus 로고
    • Fixed winding number and the quasiperiodic route to chaos in a convective fluid
    • 10.1103/PhysRevLett.55.596
    • Stavans J. Heslot F. Libchaber A. Fixed winding number and the quasiperiodic route to chaos in a convective fluid. Phys. Rev. Lett. 1985, 55:596-599. 10.1103/PhysRevLett.55.596.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 596-599
    • Stavans, J.1    Heslot, F.2    Libchaber, A.3
  • 12
    • 36149044710 scopus 로고
    • Non-linear properties of thermal convection
    • 10.1088/0034-4885/41/12/003
    • Busse F.H. Non-linear properties of thermal convection. Rep. Prog. Phys. 1978, 41:1929. 10.1088/0034-4885/41/12/003.
    • (1978) Rep. Prog. Phys. , vol.41 , pp. 1929
    • Busse, F.H.1
  • 13
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • 10.1103/RevModPhys.65.851
    • Cross M.C. Hohenberg P.C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 1993, 65:851-1112. 10.1103/RevModPhys.65.851.
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 14
    • 0025474481 scopus 로고
    • Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity
    • 10.1017/S0022112090000829
    • Nagata M. Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity. J. Fluid Mech. 1990, 217:519-527. 10.1017/S0022112090000829.
    • (1990) J. Fluid Mech. , vol.217 , pp. 519-527
    • Nagata, M.1
  • 15
    • 0041783177 scopus 로고
    • Fixed points of Turbulent Dynamical Systems and Suppression of Nonlinearity
    • J. L. Lumley, 10.1007/3-540-52535-1_47, in, edited by, Lecture Notes in Physics (Springer) Vol. 357, pp.
    • Moffatt H.K. Fixed points of Turbulent Dynamical Systems and Suppression of Nonlinearity. Whither Turbulence? Turbulence at the Crossroads 1990, 250-257. J. L. Lumley, 10.1007/3-540-52535-1_47, in edited by Lecture Notes in Physics (Springer) Vol. 357, pp.
    • (1990) Whither Turbulence? Turbulence at the Crossroads , pp. 250-257
    • Moffatt, H.K.1
  • 16
    • 0026143059 scopus 로고
    • The minimal flow unit in near-wall turbulence
    • 10.1017/S0022112091002033
    • Jiménez J. Moin P. The minimal flow unit in near-wall turbulence. J. Fluid Mech. 1991, 225:213-240. 10.1017/S0022112091002033.
    • (1991) J. Fluid Mech. , vol.225 , pp. 213-240
    • Jiménez, J.1    Moin, P.2
  • 17
    • 0028976489 scopus 로고
    • Regeneration mechanisms of near-wall turbulence structures
    • 10.1017/S0022112095000978
    • Hamilton J.M. Kim J. Waleffe F. Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 1995, 287:317-348. 10.1017/S0022112095000978.
    • (1995) J. Fluid Mech. , vol.287 , pp. 317-348
    • Hamilton, J.M.1    Kim, J.2    Waleffe, F.3
  • 18
    • 21844493361 scopus 로고
    • Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process
    • Waleffe F. Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process. Stud. Appl. Math. 1995, 95:319-343.
    • (1995) Stud. Appl. Math. , vol.95 , pp. 319-343
    • Waleffe, F.1
  • 19
    • 0037170481 scopus 로고    scopus 로고
    • Coherent structure generation in near-wall turbulence
    • 10.1017/S002211200100667X
    • Schoppa W. Hussain F. Coherent structure generation in near-wall turbulence. J. Fluid Mech. 2002, 453:57-108. 10.1017/S002211200100667X.
    • (2002) J. Fluid Mech. , vol.453 , pp. 57-108
    • Schoppa, W.1    Hussain, F.2
  • 20
    • 34748883088 scopus 로고    scopus 로고
    • Modeling transitional plane Couette flow
    • 10.1140/epjb/e2007-00243-y (Springer).
    • Lagha M. Manneville P. Modeling transitional plane Couette flow. Eur. Phys. J. B. 2007, 58:433-447. 10.1140/epjb/e2007-00243-y(Springer).
    • (2007) Eur. Phys. J. B. , vol.58 , pp. 433-447
    • Lagha, M.1    Manneville, P.2
  • 21
    • 84972308308 scopus 로고
    • The dynamics of coherent structures in the wall region of a turbulent boundary layer
    • 10.1017/S0022112088001818
    • Aubry N. Holmes P. Lumley J.L. Stone E. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 1988, 192:115-173. 10.1017/S0022112088001818.
    • (1988) J. Fluid Mech. , vol.192 , pp. 115-173
    • Aubry, N.1    Holmes, P.2    Lumley, J.L.3    Stone, E.4
  • 22
    • 27644463155 scopus 로고    scopus 로고
    • Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction
    • 10.1016/j.physd.2005.09.002
    • Smith T.R. Moehlis J. Holmes P. Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction. Physica D 2005, 211:347-376. 10.1016/j.physd.2005.09.002.
    • (2005) Physica D , vol.211 , pp. 347-376
    • Smith, T.R.1    Moehlis, J.2    Holmes, P.3
  • 23
    • 0034205196 scopus 로고    scopus 로고
    • Transition from the Couette-Taylor system to the plane Couette system
    • 10.1103/PhysRevE.61.7227
    • Faisst H. Eckhardt B. Transition from the Couette-Taylor system to the plane Couette system. Phys. Rev. E 2000, 61:7227-7230. 10.1103/PhysRevE.61.7227.
    • (2000) Phys. Rev. E , vol.61 , pp. 7227-7230
    • Faisst, H.1    Eckhardt, B.2
  • 24
    • 0347319490 scopus 로고    scopus 로고
    • Traveling waves in pipe flow
    • 10.1103/PhysRevLett.91.224502
    • Faisst H. Eckhardt B. Traveling waves in pipe flow. Phys. Rev. Lett. 2003, 91:224502. 10.1103/PhysRevLett.91.224502.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 224502
    • Faisst, H.1    Eckhardt, B.2
  • 26
    • 34547258707 scopus 로고    scopus 로고
    • Statistical analysis of coherent structures in transitional pipe flow
    • 10.1103/PhysRevE.75.066313
    • Schneider T.M. Eckhardt B. Vollmer J. Statistical analysis of coherent structures in transitional pipe flow. Phys. Rev. E 2007, 75:66313. 10.1103/PhysRevE.75.066313.
    • (2007) Phys. Rev. E , vol.75 , pp. 66313
    • Schneider, T.M.1    Eckhardt, B.2    Vollmer, J.3
  • 28
    • 33748428450 scopus 로고    scopus 로고
    • Finite lifetime of turbulence in shear flows
    • 10.1038/nature05089
    • Hof B. Westerweel J. Schneider T.M. Eckhardt B. Finite lifetime of turbulence in shear flows. Nature 2006, 443:59-62. 10.1038/nature05089.
    • (2006) Nature , vol.443 , pp. 59-62
    • Hof, B.1    Westerweel, J.2    Schneider, T.M.3    Eckhardt, B.4
  • 29
    • 55149087729 scopus 로고    scopus 로고
    • Lifetime statistics in transitional pipe flow
    • 10.1103/PhysRevE.78.046310
    • Schneider T.M. Eckhardt B. Lifetime statistics in transitional pipe flow. Phys. Rev. E 2008, 78:46310. 10.1103/PhysRevE.78.046310.
    • (2008) Phys. Rev. E , vol.78 , pp. 46310
    • Schneider, T.M.1    Eckhardt, B.2
  • 30
    • 0031205838 scopus 로고    scopus 로고
    • Tertiary and quaternary solutions for plane Couette flow
    • 10.1017/S0022112097005818
    • Clever R.M. Busse F.H. Tertiary and quaternary solutions for plane Couette flow. J. Fluid Mech. 1997, 344:137-153. 10.1017/S0022112097005818.
    • (1997) J. Fluid Mech. , vol.344 , pp. 137-153
    • Clever, R.M.1    Busse, F.H.2
  • 31
    • 85124577146 scopus 로고    scopus 로고
    • Takens-Bogdanov bifurcation of travelling-wave solutions in pipe flow
    • Mellibovsky F. Eckhardt B. Takens-Bogdanov bifurcation of travelling-wave solutions in pipe flow. J. Fluid Mech. 2010, 670:26.
    • (2010) J. Fluid Mech. , vol.670 , pp. 26
    • Mellibovsky, F.1    Eckhardt, B.2
  • 32
    • 84869780600 scopus 로고    scopus 로고
    • From travelling waves to mild chaos: A supercritical bifurcation cascade in pipe flow
    • 10.1017/jfm.2012.326, J. Fluid Mech. Available on CJ02012, doi:.
    • Mellibovsky F. Eckhardt B. From travelling waves to mild chaos: A supercritical bifurcation cascade in pipe flow. 10.1017/jfm.2012.326J. Fluid Mech. Available on CJ02012, doi:.
    • Mellibovsky, F.1    Eckhardt, B.2
  • 33
    • 0000549680 scopus 로고
    • Invariant measurement of strange sets in terms of cycles
    • 10.1103/PhysRevLett.61.2729
    • Cvitanović P. Invariant measurement of strange sets in terms of cycles. Phys. Rev. Lett. 1988, 61:2729-2732. 10.1103/PhysRevLett.61.2729.
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 2729-2732
    • Cvitanović, P.1
  • 34
    • 0000540018 scopus 로고
    • Periodic orbit analysis of the Lorenz attractor
    • 10.1007/BF01316970
    • Eckhardt B. Ott G. Periodic orbit analysis of the Lorenz attractor. Z. Phys. B 1994, 93:259-266. 10.1007/BF01316970.
    • (1994) Z. Phys. B , vol.93 , pp. 259-266
    • Eckhardt, B.1    Ott, G.2
  • 35
    • 0002099058 scopus 로고    scopus 로고
    • Hopf's last hope: Spatiotemporal chaos in terms of unstable recurrent patterns
    • 10.1088/0951-7715/10/1/004
    • Christiansen F. Cvitanović P. Putkaradze V. Hopf's last hope: Spatiotemporal chaos in terms of unstable recurrent patterns. Nonlinearity 1997, 10:55. 10.1088/0951-7715/10/1/004.
    • (1997) Nonlinearity , vol.10 , pp. 55
    • Christiansen, F.1    Cvitanović, P.2    Putkaradze, V.3
  • 36
    • 0035951045 scopus 로고    scopus 로고
    • Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst
    • 10.1017/S0022112001006243
    • Kawahara G. Kida S. Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst. J. Fluid Mech. 2001, 449:291-300. 10.1017/S0022112001006243.
    • (2001) J. Fluid Mech. , vol.449 , pp. 291-300
    • Kawahara, G.1    Kida, S.2
  • 37
    • 34547264698 scopus 로고    scopus 로고
    • Recurrent motions within plane Couette turbulence
    • 10.1017/S0022112007005459
    • Viswanath D. Recurrent motions within plane Couette turbulence. J. Fluid Mech. 2007, 580:339-358. 10.1017/S0022112007005459.
    • (2007) J. Fluid Mech. , vol.580 , pp. 339-358
    • Viswanath, D.1
  • 38
    • 79551580536 scopus 로고    scopus 로고
    • Geometry of the turbulence in wall-bounded shear flows: Periodic orbits
    • 10.1088/0031-8949/2010/T142/014007
    • Cvitanović P. Gibson J.F. Geometry of the turbulence in wall-bounded shear flows: Periodic orbits. Phys. Scr. 2010, T142:014007. 10.1088/0031-8949/2010/T142/014007.
    • (2010) Phys. Scr. , vol.T142 , pp. 014007
    • Cvitanović, P.1    Gibson, J.F.2
  • 39
    • 84871870290 scopus 로고    scopus 로고
    • Channelflow Website
    • see for
    • Gibson J.F. Channelflow Website. 2011, see for
    • (2011)
    • Gibson, J.F.1
  • 40
    • 0001367536 scopus 로고    scopus 로고
    • Fractal stability border in plane Couette flow
    • 10.1103/PhysRevLett.79.5250
    • Schmiegel A. Eckhardt B. Fractal stability border in plane Couette flow. Phys. Rev. Lett. 1997, 79:5250-5253. 10.1103/PhysRevLett.79.5250.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 5250-5253
    • Schmiegel, A.1    Eckhardt, B.2
  • 41
    • 50949126837 scopus 로고    scopus 로고
    • Visualizing the geometry of state space in plane Couette flow
    • 10.1017/S002211200800267X
    • Gibson J.F. Halcrow J. Cvitanović P. Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 2008, 611:107-130. 10.1017/S002211200800267X.
    • (2008) J. Fluid Mech. , vol.611 , pp. 107-130
    • Gibson, J.F.1    Halcrow, J.2    Cvitanović, P.3
  • 43
    • 70350641232 scopus 로고    scopus 로고
    • Shear-flow transition: The basin boundary
    • 10.1088/0951-7715/22/11/004
    • Lebovitz N.R. Shear-flow transition: The basin boundary. Nonlinearity 2009, 22:2645. 10.1088/0951-7715/22/11/004.
    • (2009) Nonlinearity , vol.22 , pp. 2645
    • Lebovitz, N.R.1
  • 44
    • 82955248047 scopus 로고    scopus 로고
    • Boundary collapse in models of shear-flow transition
    • 10.1016/j.cnsns.2011.07.023
    • Lebovitz N.R. Boundary collapse in models of shear-flow transition. Commun. Nonlinear Sci. Numer. Simul. 2012, 17:2095-2100. 10.1016/j.cnsns.2011.07.023.
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 2095-2100
    • Lebovitz, N.R.1
  • 45
    • 34547240198 scopus 로고    scopus 로고
    • Lower branch coherent states in shear flows: Transition and control
    • 10.1103/PhysRevLett.98.204501
    • Wang J. Gibson J.F. Waleffe F. Lower branch coherent states in shear flows: Transition and control. Phys. Rev. Lett. 2007, 98:204501. 10.1103/PhysRevLett.98.204501.
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 204501
    • Wang, J.1    Gibson, J.F.2    Waleffe, F.3
  • 46
    • 80052452844 scopus 로고    scopus 로고
    • Homoclinic tangle on the edge of shear turbulence
    • 10.1103/PhysRevLett.107.114501
    • van Veen L. Kawahara G. Homoclinic tangle on the edge of shear turbulence. Phys. Rev. Lett. 2011, 107:114501. 10.1103/PhysRevLett.107.114501.
    • (2011) Phys. Rev. Lett. , vol.107 , pp. 114501
    • van Veen, L.1    Kawahara, G.2
  • 47
    • 62149120529 scopus 로고    scopus 로고
    • Basin boundary, edge of chaosedge state in a two-dimensional model
    • 10.1088/1367-2630/11/1/013040
    • Vollmer J. Schneider T.M. Eckhardt B. Basin boundary, edge of chaosedge state in a two-dimensional model. New J. Phys. 2009, 11:1-23. 10.1088/1367-2630/11/1/013040.
    • (2009) New J. Phys. , vol.11 , pp. 1-23
    • Vollmer, J.1    Schneider, T.M.2    Eckhardt, B.3
  • 48
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractorstransient chaos
    • 10.1016/0167-2789(83)90126-4
    • Grebogi C. Ott E. Yorke J.A. Crises, sudden changes in chaotic attractorstransient chaos. Physica D 1983, 7:181-200. 10.1016/0167-2789(83)90126-4.
    • (1983) Physica D , vol.7 , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 49
    • 0015858113 scopus 로고
    • On finite limit sets for transformations on the unit interval
    • 10.1016/0097-3165(73)90033-2
    • Metropolis N. Stein M.L. Stein P.R. On finite limit sets for transformations on the unit interval. J. Comb. Theory, Ser. A 1973, 44:25-44. 10.1016/0097-3165(73)90033-2.
    • (1973) J. Comb. Theory, Ser. A , vol.44 , pp. 25-44
    • Metropolis, N.1    Stein, M.L.2    Stein, P.R.3
  • 50
    • 29644442802 scopus 로고    scopus 로고
    • Periodic motion representing isotropic turbulence
    • 10.1016/j.fluiddyn.2005.09.001
    • van Veen L. Kida S. Kawahara G. Periodic motion representing isotropic turbulence. Fluid Dyn. Res. 2006, 38:19-46. 10.1016/j.fluiddyn.2005.09.001.
    • (2006) Fluid Dyn. Res. , vol.38 , pp. 19-46
    • van Veen, L.1    Kida, S.2    Kawahara, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.