Bifurcations in rotating spherical shell convection under the influence of differential rotation. (English) Zbl 07871535
References:
| [1] | Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, 1961, Oxford University Press: Oxford University Press, New York · Zbl 0142.44103 |
| [2] | Roberts, P. H., On the thermal instability of rotating-fluid sphere containing heat sources, Phil. Trans. R. Soc. London A, 263, 93-117, 1968 · Zbl 0207.26903 · doi:10.1098/rsta.1968.0007 |
| [3] | Busse, F. H., Thermal instabilities in rapidly rotating systems, J. Fluid Mech., 44, 441-460, 1970 · Zbl 0224.76041 · doi:10.1017/S0022112070001921 |
| [4] | Geiger, G.; Busse, F. H., On the onset of thermal convection in slowly rotating fluid shells, Geophys. Astrophys. Fluid Dynam., 18, 147-156, 1981 · Zbl 0467.76077 · doi:10.1080/03091928108208777 |
| [5] | Bercovici, D.; Schubert, G.; Glatzmaier, G. A.; Zebib, A., Three-dimensional thermal convection in a spherical shell, J. Fluid Mech., 206, 75-104, 1989 · Zbl 0678.76087 · doi:10.1017/S0022112089002235 |
| [6] | Sun, Z.-P.; Schubert, G.; Glatzmaier, G. A., Transition to chaotic thermal convection in a rapidly rotating spherical fluid shell, Geophys. Astrophys. Fluid Dynam., 69, 95-131, 1993 · doi:10.1080/03091929308203576 |
| [7] | Ardes, M.; Busse, F. H.; Wicht, J., Thermal convection in rotating spherical shells, Phys. Earth Planet Inter., 99, 55-67, 1997 · doi:10.1016/S0031-9201(96)03200-1 |
| [8] | Kitauchi, H.; Araki, K.; Kida, S., Flow structure of thermal convection in a rotating spherical shell, Nonlinearity, 10, 885-904, 1997 · Zbl 0911.76085 · doi:10.1088/0951-7715/10/4/005 |
| [9] | Simitev, R.; Busse, F. H., Patterns of convection in rotating spherical shells, New J. Phys., 5, 97, 2003 · doi:10.1088/1367-2630/5/1/397 |
| [10] | Al-Shamali, F. M.; Heimpel, M. H.; Aurnou, J. M., Varying the spherical shell geometry in rotating thermal convection, Geophys. Astrophys. Fluid Dyn., 98, 153-169, 2004 · doi:10.1080/03091920410001659281 |
| [11] | Kimura, K.; Takehiro, S. I.; Yamada, M., Stability and bifurcation diagram of Boussinesq thermal convection in a moderately rotating spherical shell, Phys. Fluids, 23, 074101, 2011 · doi:10.1063/1.3602917 |
| [12] | Li, L.; X. Liao, Z. P.; Zhang, K., Multiplicity of nonlinear thermal convection in a spherical shell, Phys. Rev. E, 71, 016301, 2005 · doi:10.1103/PhysRevE.71.016301 |
| [13] | Borońska, K.; Tuckerman, L. S., Extreme multiplicity in cylindrical Rayleigh-Bénard convection. II. Bifurcation diagram and symmetry classification, Phys. Rev. E, 81, 036321, 2010 · doi:10.1103/PhysRevE.81.036321 |
| [14] | Feudel, F.; Bergemann, K.; Tuckerman, L. S.; Egbers, C.; Futterer, B.; Gellert, M.; Hollerbach, R., Convection patterns in a spherical fluid shell, Phys. Rev. E, 83, 046304, 2011 · doi:10.1103/PhysRevE.83.046304 |
| [15] | Feudel, F.; Seehafer, N.; Tuckerman, L. S.; Gellert, M., Multistability in rotating spherical shell convection, Phys. Rev. E, 87, 023021, 2013 · doi:10.1103/PhysRevE.87.023021 |
| [16] | Feudel, F.; Tuckerman, L. S.; Gellert, M.; Seehafer, N., Bifurcations of rotating waves in rotating spherical shell convection, Phys. Rev. E, 92, 053015, 2015 · doi:10.1103/PhysRevE.92.053015 |
| [17] | Mannic, P. M.; Mestel, A. J., Weakly nonlinear mode interactions in spherical Rayleigh-Bénard convection, J. Fluid Mech., 874, 359-390, 2019 · Zbl 1419.76590 · doi:10.1017/jfm.2019.440 |
| [18] | Travnikov, V.; Zaussinger, F.; Beltrame, P.; Egbers, C., Influence of the temperature-dependent viscosity on convective flow in the radial force field, Phys. Rev. E, 96, 023108, 2017 · doi:10.1103/PhysRevE.96.023108 |
| [19] | Grossmann, S.; Lohse, D.; Sun, C., High Reynolds number Taylor-Couette turbulence, Annu. Rev. Fluid Mech., 48, 53-80, 2016 · Zbl 1356.76106 · doi:10.1146/annurev-fluid-122414-034353 |
| [20] | Andereck, C. D. and Hayot, F., Ordered and Turbulent Patterns in Taylor-Couette Flow, NATO ASI Series B Physics Vol. 297 (Springer, New York, 1992). |
| [21] | Gollub, J. P.; Swinney, H., Onset of turbulence in a rotating fluid, Phys. Rev. Lett., 35, 927-930, 1975 · doi:10.1103/PhysRevLett.35.927 |
| [22] | Newhouse, S. E.; Ruelle, D.; Takens, F., Occurrence of strange axiom a attractors near quasiperiodic flow on \(t^m,m\geq3\), Commun. Math. Phys., 64, 35-40, 1978 · Zbl 0396.58029 · doi:10.1007/BF01940759 |
| [23] | Marcus, P. S.; Tuckerman, L. S., Simulation of flow between concentric rotating spheres. Part 1. Steady states, J. Fluid Mech., 185, 1-30, 1987 · Zbl 0645.76117 · doi:10.1017/S0022112087003069 |
| [24] | Marcus, P. S.; Tuckerman, L. S., Simulation of flow between concentric rotating spheres. Part 2. Transitions, J. Fluid Mech., 185, 31-65, 1987 · Zbl 0645.76118 · doi:10.1017/S0022112087003070 |
| [25] | Hollerbach, R., Instabilities of the Stewartson layer. Part 1. The dependence on the sign of \(Ro\), J. Fluid Mech., 492, 289-302, 2003 · Zbl 1063.76558 · doi:10.1017/S0022112003005676 |
| [26] | Hoff, M.; Harlander, U., Stewartson-layer instability in a wide-gap spherical Couette experiment: Rossby number dependence, J. Fluid Mech., 878, 522-543, 2019 · Zbl 1430.76178 · doi:10.1017/jfm.2019.636 |
| [27] | Mannix, P.-M.; Mestel, A.-J., Bistability and hysteresis of axisymmetric thermal convection between differentially rotating spheres, J. Fluid Mech., 911, A12, 2021 · Zbl 1461.76420 · doi:10.1017/jfm.2020.1042 |
| [28] | P.-J. Holmes, G. J., Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Applied Mathematical Sciences Vol. 42 (Springer, New York, 1983). · Zbl 0515.34001 |
| [29] | Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, Applied Mathematical Sciences Vol. 112 (Springer, New York, 2004). · Zbl 1082.37002 |
| [30] | Tuckerman, L. S.; Barkley, D., Global bifurcation to travelling waves in axisymmetric convection, Phys. Rev. Lett., 61, 408-411, 1988 · doi:10.1103/PhysRevLett.61.408 |
| [31] | Kevrekidis, I. G.; Rico/Martinez, R.; Ecke, R. E.; Farber, R. M.; Lapedes, A. S., Global bifurcations in Rayleigh-Bénad convection. Experiments, empirical maps and numerical bifurcation analysis, Physica D, 71, 342-362, 1994 · Zbl 0825.76228 · doi:10.1016/0167-2789(94)90152-X |
| [32] | Mullin, T., Finite-dimensional dynamics in Taylor-Couette flow, IMA J. Appl. Maths, 46, 109-119, 1991 · Zbl 0718.76115 · doi:10.1093/imamat/46.1-2.109 |
| [33] | Lopez, J.-M.; Marquese, F.; Shen, J., Complex dynamics in a short annular container with rotating bottom and inner cylinder, J. Fluid Mech., 501, 327-354, 2004 · Zbl 1071.76064 · doi:10.1017/S0022112003007493 |
| [34] | Crawford, J. D.; Knobloch, E., Symmetry and symmetry-breaking bifurcations in fluid dynamics, Annu. Rev. Fluid Dyn., 23, 341-387, 1991 · Zbl 0717.76007 · doi:10.1146/annurev.fl.23.010191.002013 |
| [35] | Afraimovich, V. S. and Shil’nikov, L. P., “Invariant two-dimensional tori, their destruction and stochasticity,” Technical Report (Gorkii University, 1983). |
| [36] | Ostlund, S.; Rand, D.; Sethna, J.; Siggia, E. D., Universal transition from quasiperiodicity to chaos in dissipative systems, Physica D, 8, 303-342, 1983 · Zbl 0538.58025 · doi:10.1016/0167-2789(83)90229-4 |
| [37] | Anishchenko, V. S.; Safonova, M. A., Mechanism of destruction of invariant curve in a model map of the plane, Radiotekh. Elektron., 32, 1207-1216, 1987 |
| [38] | Abshagen, J.; Lopez, J. M.; Marques, F.; Pfister, G., Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics, Phys. Rev. Lett., 94, 074501, 2005 · doi:10.1103/PhysRevLett.94.074501 |
| [39] | Feudel, F.; Tuckerman, L. S.; Zaks, M.; Hollerbach, R., Hysteresis of dynamos in rotating spherical shell convection, Phys. Rev. Fluids, 2, 053902, 2017 · doi:10.1103/PhysRevFluids.2.053902 |
| [40] | Ecke, R. E.; Zhong, F.; Knobloch, E., Hopf bifurcation with broken reflection symmetry in rotating Rayleigh-Bénard convection, Europhys. Lett., 19, 177-182, 1992 · doi:10.1209/0295-5075/19/3/005 |
| [41] | Knobloch, E., “Bifurcations in rotating systems,” in Lectures on Solar and Planetary Dynamos, edited by M. R. E. Proctor and A. D. Gilbert (Cambridge University Press, Cambridge, 1994), pp. 331-372. · Zbl 0861.76089 |
| [42] | Christensen, U.; Aubert, J.; Cardin, P.; Dormy, E.; Gibbons, S.; Glatzmaier, G.; Grote, E.; Honkura, Y.; Jones, C.; Kono, M.; Matsushima, M.; Sakuraba, A.; Takahashi, F.; Tilgner, A.; Wicht, J.; Zhang, K., A numerical dynamo benchmark, Phys. Earth Planet. Inter., 128, 25-34, 2001 · doi:10.1016/S0031-9201(01)00275-8 |
| [43] | Matsui, H.; Heien, E.; Aubert, J.; Aurnou, J. M.; Avery, M.; Brown, B.; Buffett, B. A.; Busse, F.; Christensen, U. R.; Davies, C. J.; Featherstone, N.; Gastine, T.; Glatzmaier, G. A.; Gubbins, D.; Guermond, J.-L.; Hayashi, Y.-Y.; Hollerbach, R.; Hwang, L. J.; Jackson, A.; Jones, C. A.; Jiang, W.; Kellogg, L. H.; Kuang, W.; Landeau, M.; Marti, P.; Olson, P.; Ribeiro, A.; Sasaki, Y.; Schaeffer, N.; Simitev, R. D.; Sheyko, A.; Silva, L.; Stanley, S.; Takahashi, F.; Takehiro, S.; Wicht, J.; Willis, A. P., Performance benchmarks for a next generation numerical dynamo model, Geochem. Geophys. Geosyst., 17, 1586-1607, 2016 · doi:10.1002/2015GC006159 |
| [44] | Hollerbach, R., A spectral solution of the magneto-convection equations in spherical geometry, Int. J. Num. Meth. Fluids, 32, 773-797, 2000 · Zbl 0958.76065 · doi:10.1002/(SICI)1097-0363(20000415)32:7<773::AID-FLD988>3.0.CO;2-P |
| [45] | Mamun, C. K.; Tuckerman, L. S., Asymmetry and Hopf bifurcation in spherical Couette flow, Phys. Fluids, 7, 80-91, 1995 · Zbl 0836.76033 · doi:10.1063/1.868730 |
| [46] | Feudel, U.; Jansen, W., CANDYS/QA—A software system for qualitative analysis of nonlinear dynamical systems, Int. J. Bifurcation Chaos, 2, 773-794, 1992 · Zbl 0872.65059 · doi:10.1142/S0218127492000434 |
| [47] | Meca, E.; Mercader, I.; Batiste, O.; Ramirez-Piscina, L., Complex dynamics in double-diffusive convection, Theoret. Comput. Fluid Dyn., 18, 231-238, 2004 · Zbl 1178.76152 · doi:10.1007/s00162-004-0129-1 |
| [48] | Busse, F. H., Convection driven zonal flows and vortices in the major planets, Chaos, 4, 123-134, 1994 · doi:10.1063/1.165999 |
| [49] | Khibnik, A. I., “LINLBF: A program for continuation and bifurcation analysis of equilibria up to codimension three,” in Continuation and Bifurcations: Numerical Techniques and Applications (Kluwer Academic Publisher, 1989), pp. 283-296. · Zbl 0705.34001 |
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