메뉴 건너뛰기




Volumn 17, Issue 6, 2005, Pages 1-10

Experimental observation of near-heteroclinic cycles in the von Kármán swirling flow

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; REYNOLDS NUMBER; ROTATING DISKS; SWIRLING FLOW; VELOCITY MEASUREMENT; VISUALIZATION; WAVE EFFECTS;

EID: 21244434315     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1926827     Document Type: Article
Times cited : (23)

References (29)
  • 3
    • 84974489205 scopus 로고
    • "Asymptotic stability of heteroclinic cycles in systems with symmetry"
    • ZZZZZZ 0143-3857
    • M. Krupa and I. Melbourne, "Asymptotic stability of heteroclinic cycles in systems with symmetry," Ergod. Theory Dyn. Syst. ZZZZZZ 0143-3857 15, 121 (1995).
    • (1995) Ergod. Theory Dyn. Syst. , vol.15 , pp. 121
    • Krupa, M.1    Melbourne, I.2
  • 4
    • 0001225644 scopus 로고    scopus 로고
    • "Robust heteroclinic cycles"
    • JNSCEK 0938-894
    • M. Krupa, "Robust heteroclinic cycles," J. Nonlinear Sci. JNSCEK 0938-8794 7, 129 (1997).
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 129
    • Krupa, M.1
  • 5
    • 0001218019 scopus 로고
    • "Convection in a rotating layer: A simple case of turbulence"
    • SCIEAS 0036-8075
    • F. H. Busse and K. E. Heikes, "Convection in a rotating layer: A simple case of turbulence," Science SCIEAS 0036-8075 208, 173 (1980).
    • (1980) Science , vol.208 , pp. 173
    • Busse, F.H.1    Heikes, K.E.2
  • 6
    • 0014467322 scopus 로고
    • "Transition from laminar convection to thermal turbulence in a rotating fluid layer"
    • JFLSA7 0022-1120
    • G. Küppers and D. Lortz, "Transition from laminar convection to thermal turbulence in a rotating fluid layer," J. Fluid Mech. JFLSA7 0022-1120 35, 609 (1969).
    • (1969) J. Fluid Mech. , vol.35 , pp. 609
    • Küppers, G.1    Lortz, D.2
  • 7
    • 0000268789 scopus 로고
    • "Nonlinear aspects of competition between three species"
    • SMJMAP 0036-1399 10.1137/01022
    • R. M. May and W. J. Leonard, "Nonlinear aspects of competition between three species," SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0129022 29, 243 (1975).
    • (1975) SIAM Appl. Math. , vol.29 , pp. 243
    • May, R.M.1    Leonard, W.J.2
  • 8
    • 0001073293 scopus 로고
    • "Strong spatial resonance and travelling waves in Bénard convection"
    • APYLAAG 0375-9601 10.1016/0375-9601(87)90008-9
    • C. A. Jones and M. R. E. Proctor, "Strong spatial resonance and travelling waves in Bénard convection," Phys. Lett. APYLAAG 0375-9601 10.1016/0375-9601(87)90008-9 121, 224 (1987).
    • (1987) Phys. Lett. A , vol.121 , pp. 224
    • Jones, C.A.1    Proctor, M.R.2
  • 9
    • 84971848073 scopus 로고
    • "The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance"
    • JFLSA7 0022-1120
    • M. R. E. Proctor and C. A. Jones, "The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance," J. Fluid Mech. JFLSA7 0022-1120 188, 301 (1988).
    • (1988) J. Fluid Mech. , vol.188 , pp. 301
    • Proctor, M.R.1    Jones, C.A.2
  • 10
    • 45549113061 scopus 로고
    • "Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry"
    • PDNPDT 0167-2789 10.1016/0167-2789(88)90032-2
    • D. Armbruster, J. Guckenheimer, and P. Holmes, "Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry," Physica DPDNPDT 0167-2789 10.1016/0167-2789(88)90032-2 29, 257 (1988).
    • (1988) Physica D , vol.29 , pp. 257
    • Armbruster, D.1    Guckenheimer, J.2    Holmes, P.3
  • 11
    • 0002766333 scopus 로고    scopus 로고
    • "Mode interactions in Rayleigh-Bénard convection"
    • PDNPDT 0167-2789 10.1016/0167-2789(96)00041-3
    • S. Cox, "Mode interactions in Rayleigh-Bénard convection," Physica DPDNPDT 0167-2789 10.1016/0167-2789(96)00041-3 95, 50 (1996).
    • (1996) Physica D , vol.95 , pp. 50
    • Cox, S.1
  • 12
    • 0036876571 scopus 로고    scopus 로고
    • "Robust heteroclinic cycles in two-dimensional Rayleigh-Bénard convection without Boussinesq symmetry"
    • IJBEE4 0218-1274
    • I. Mercader, J. Prat, and E. Knobloch, "Robust heteroclinic cycles in two-dimensional Rayleigh-Bénard convection without Boussinesq symmetry," Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 12, 2501 (2002).
    • (2002) Int. Bifurcation Chaos Appl. Sci. Eng. , vol.12 , pp. 2501
    • Mercader, I.1    Prat, J.2    Knobloch, E.3
  • 13
    • 84972308308 scopus 로고
    • "The dynamics of coherent structures in the wall region of a turbulent boundary layer"
    • JFLSA7 0022-1120
    • N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, "The dynamics of coherent structures in the wall region of a turbulent boundary layer," J. Fluid Mech. JFLSA7 0022-1120 92, 115 (1988).
    • (1988) Fluid Mech. , vol.92 , pp. 115
    • Aubry, N.1    Holmes, P.2    Lumley, J.L.3    Stone, E.4
  • 15
    • 0025448183 scopus 로고
    • "Back in the saddle again: A computer assisted study of the Kuramoto-Sivashinsky equation"
    • SMJMAP 0036-1399 10.1137/0150045
    • I. G. Kevrekidis, B. Nicolaenko, and J. C. Scovel, "Back in the saddle again: A computer assisted study of the Kuramoto-Sivashinsky equation," SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0150045 50, 760 (1990).
    • (1990) SIAM Appl. Math. , vol.50 , pp. 760
    • Kevrekidis, I.G.1    Nicolaenko, B.2    Scovel, J.C.3
  • 16
    • 0032209440 scopus 로고    scopus 로고
    • "Convection under rotation for Prandtl numbers near 1: Küppers-Lortz instability"
    • PLEEE8 1063-651X 10.1103/PhysRev.58.5821
    • Y. Hu, W. Pesch, G. Ahlers, and R. E. Ecke, "Convection under rotation for Prandtl numbers near 1: Küppers-Lortz instability," Phys. Rev. EPLEEE8 1063-651X 10.1103/PhysRevE.58.5821 58, 5821 (1998).
    • (1998) Phys. Rev. E , vol.58 , pp. 21
    • Hu, Y.1    Pesch, W.2    Ahlers, G.3    Ecke, R.E.4
  • 17
    • 0000667473 scopus 로고    scopus 로고
    • "Identification of intermittent ordered patterns as heteroclinic connections"
    • PRLTAO 0031-9007 10.1103/PhysRevLett.76.2061
    • E. Stone, M. Gorman, M. El Hamdi, and K. A. Robbins, "Identification of intermittent ordered patterns as heteroclinic connections," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/ PhysRevLett.76.2061 76, 2061 (1996).
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 2061
    • Stone, E.1    Gorman, M.2    El Hamdi, M.3    Robbins, K.A.4
  • 18
    • 0242449865 scopus 로고    scopus 로고
    • "Cellular pattern formation in circular domains"
    • CHAOEH 1054-1500 10.1063/1.166218
    • A. Palacios, G. H. Gunaratne, and M. Gorman, "Cellular pattern formation in circular domains," Chaos CHAOEH 1054-1500 10.1063/ 1.166218 7, 463 (1997).
    • (1997) Chaos , vol.7 , pp. 463
    • Palacios, A.1    Gunaratne, G.H.2    Gorman, M.3
  • 19
    • 0037465213 scopus 로고    scopus 로고
    • "The 1:2 mode interaction in exactly counter-rotating von Kármán swirling flow"
    • JFLSA7 0022-1120 10.1017/S002211200075
    • C. Nore, L. S. Tuckerman, O. Daube, and S. Xin, "The 1:2 mode interaction in exactly counter-rotating von Kármán swirling flow," J. Fluid Mech. JFLSA7 0022-1120 10.1017/ S0022112002003075 477, 51 (2003).
    • (2003) J. Fluid Mech. , vol.477 , pp. 51
    • Nore, C.1    Tuckerman, L.S.2    Daube, O.3    Xin, S.4
  • 20
    • 0037171419 scopus 로고    scopus 로고
    • "Mode interactions in an enclosed swirling flow: A double Hopf bifurcation between azimuthal wavenumbers 0 and 2"
    • JFLSA7 0022-1120 10.1017/S0022112001007285
    • F. Marques, J. M. Lopez, and J. Shen, "Mode interactions in an enclosed swirling flow: A double Hopf bifurcation between azimuthal wavenumbers 0 and 2," J. Fluid Mech. JFLSA7 0022-1120 10.1017/ S0022112001007285 455, 263 (2002).
    • (2002) Fluid Mech. , vol.455 , pp. 263
    • Marques, F.1    Lopez, J.M.2    Shen, J.3
  • 21
    • 0037055082 scopus 로고    scopus 로고
    • "Instability and mode interactions in a differentially driven rotating cylinder"
    • JFLSA7 0022-1120 10.1017/S0022112002008649
    • J. M. Lopez, J. E. Hart, F. Marques, S. Kittelman, and J. Shen, "Instability and mode interactions in a differentially driven rotating cylinder," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112002008649 462, 383 (2002).
    • (2002) Fluid Mech. , vol.462 , pp. 383
    • Lopez, J.M.1    Hart, J.E.2    Marques, F.3    Kittelman, S.4    Shen, J.5
  • 22
    • 13444255331 scopus 로고    scopus 로고
    • "Tangent double Hopf bifurcation in a differentially rotating cylinder flow"
    • PLEEE8 1063-651X 10.1103/PhysRevE.68.016310
    • F. Marques, A. Yu. Gelfgat, and J. M. Lopez, "Tangent double Hopf bifurcation in a differentially rotating cylinder flow," Phys. Rev. EPLEEE8 1063-651X 10.1103/PhysRevE.68.016310 68, 016310 (2003).
    • (2003) Phys. Rev. E , vol.68 , pp. 016310
    • Marques, F.1    Gelfgat, A.Yu.2    Lopez, J.M.3
  • 23
    • 2642531243 scopus 로고    scopus 로고
    • "Experimental and numerical study of the shear layer instability between two counter-rotating disks"
    • JFLSA7 0022-1120
    • F. Moisy, O. Doaré, T. Pasutto, O. Daube, and M. Rabaud, "Experimental and numerical study of the shear layer instability between two counter-rotating disks," J. Fluid Mech. JFLSA7 0022-1120 507, 175 (2004).
    • (2004) J. Fluid Mech. , vol.507 , pp. 175
    • Moisy, F.1    Doaré, O.2    Pasutto, T.3    Daube, O.4    Rabaud, M.5
  • 24
    • 2542514650 scopus 로고    scopus 로고
    • "Mode competition between rotating waves in a swirling flow with reflection symmetry"
    • JFLSA7 0022-1120
    • J. M. Lopez and F. Marques, "Mode competition between rotating waves in a swirling flow with reflection symmetry," J. Fluid Mech. JFLSA7 0022-1120 507, 265 (2004).
    • (2004) Fluid Mech. , vol.507 , pp. 265
    • Lopez, J.M.1    Marques, F.2
  • 25
    • 2642547323 scopus 로고    scopus 로고
    • "Survey of instability thresholds of flow between exactly counter-rotating disks"
    • JFLSA7 0022-1120
    • C. Nore, M. Tartar, O. Daube, and L. S. Tuckerman, "Survey of instability thresholds of flow between exactly counter-rotating disks," J. Fluid Mech. JFLSA7 0022-1120 511, 45 (2004).
    • (2004) J. Fluid Mech. , vol.511 , pp. 45
    • Nore, C.1    Tartar, M.2    Daube, O.3    Tuckerman, L.S.4
  • 26
    • 0001295962 scopus 로고
    • "Instabilities of one-dimensional cellular patterns"
    • PRLTAO 0031-9007 10.1103/PhysRevLett.64.866
    • P. Coullet and G. Iooss, "Instabilities of one-dimensional cellular patterns," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/ PhysRevLett.64.866 64, 866 (1990).
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 866
    • Coullet, P.1    Iooss, G.2
  • 27
    • 21244506449 scopus 로고    scopus 로고
    • note
    • Comparison with the numerical computation [see Fig, 16(c) in the paper of Nore et al (ref. 19) allow us to further identity the orientation of the observed states P and P′. The velocity field of the state P [fig. 11(a) ] shows a unique hyperbolic center (x,z) = (0,0), induicating that the two peripherical hyperbolic point H and H* are close to the PIV plane where the measurements are performed [see Fig. 12 (a)]. On the other hand, two hyperbolic points can be seen near the cylinder axis for the state p′ [Fig. 11 (c) indicating that the PIV plane now cuts through the two elliptic points E and E* [see Fig. 12 (c)
  • 28
    • 0025447065 scopus 로고
    • "Random perturbations of heteroclinic attractors"
    • SMJMAP 0036-1399 10.1137/01043
    • E. Stone and P. Holmes, "Random perturbations of heteroclinic attractors," SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0150043 50, 726 (1990).
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 726
    • Stone, E.1    Holmes, P.2
  • 29
    • 14044258450 scopus 로고    scopus 로고
    • "Dynamics in the 1:2 spatial resonance with broken reflection symmetry"
    • PDNPDT 0167-2789
    • J. Porter and E. Knobloch, "Dynamics in the 1:2 spatial resonance with broken reflection symmetry," Physica DPDNPDT 0167-2789 201, 318 (2005).
    • (2005) Physica D , vol.201 , pp. 318
    • Porter, J.1    Knobloch, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.