Abstract
A new heteroclinic cycle is demonstrated in the case of thermal convection in a layer heated from below and rotating about a horizontal axis. This system can be realized experimentally through the use of the centrifugal force as effective gravity in the system of the rotating cylindrical annulus.
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References
KRUPA, M., Robust heteroclinic cycles, J. Nonlinear Sci., 7, 129–176, 1997.
KüPPERS, G., AND LORTZ, D., Transition from laminar convection to thermal turbulence in a rotating fluid layer, J. Fluid Mech., 35, 609–620, 1969.
BUSSE, F.H., AND CLEVER, R.M., Nonstationary convection in a rotating system, 376–385 in Recent Developments in Theoretical and Experimental Fluid Mechanics, U. Müller, K.G. Roesner, B. Schmidt, eds., Springer, 1979.
BUSSE, F.H., Transition to turbulence via the statistical limit cycle route, 197–202 in Turbulence and Chaotic Phenomena in Fluids, T. Tatsumi, ed., Elsevier, 1984.
Tu, Y., AND CROSS, M.C., Chaotic Domain Structure in Rotating Convection, Phys. Rev. Lett., 69, 2515–2518, 1992.
BUSSE, F.H., AND HEIKES, K.E., Convection in a rotating layer: A simple case of turbulence, SCIENCE, 208, 173–175, 1980.
HEIKES, K.E., AND BUSSE, F.H., Weakly nonlinear turbulence in a rotating convection layer, Annals N.Y. Academy of Sciences, 357, 28–36, 1980.
ZHONG, F., ECKE, R.E., AND STEINBERG, V., Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection, Phys. Rev. Lett., 67, 2473–2476, 1991.
Hu, Y., ECKE, R.E., AND AHLERS, G., Time and Length Scales in Rotating Rayleigh-Bénard Convection, Phys. Rev. Lett., 74, 5040–5043, 1995.
Hu, Y., ECKE, R.E., AND AHLERS, G., Convection under rotation for Prandtl numbers near 1: Linear stability, wavenumber selection and pattern dynamics, Phys. Rev. E, 55, 6928–6949, 1997.
MlLLàN-RODRIGUEZ, J., BESTEHORN, M., PéREZ-GARCiA, C., FRIEDRICH, R., AND NEUFELD, M., Defect motion in rotating fluids, Phys. Rev. Lett., 74, 530–533, 1995.
PESCH, W., Complex spatio-temporal convection patterns, CHAOS, 6, 348–357, 1996.
AUER, M., BUSSE, F.H., AND CLEVER, R.M., Three-dimensional convection driven by centrifugal buoyancy, J. Fluid Mech., 301, 371–382, 1995.
JALETZKY, M., AND BUSSE, F.H., New Pattern of Convection Driven by Centrifugal Buoyancy, ZAMM, to be published, 1998.
BUSSE, F.H., Thermal instabilities in rapidly rotating systems, J. Fluid Mech., 44, 441–460, 1970.
SCHLüTER, A., LORTZ, D., AND BUSSE, F., On the stability of steady finite amplitude convection, J. Fluid Mech., 23, 129–144, 1965.
CLEVER, R.M., AND BUSSE, F.H., Steady and Oscillatory Bimodal Convection, J. Fluid Mech., 271, 103–118, 1994.
CLEVER, R.M., AND BUSSE, F.H., Standing and Oscillatory Blob Convection, J. Fluid Mech., 297, 255–273, 1995.
SCHMITT, B.J., AND WAHL, W. Von, Decomposition of Solenoidal Fields into Poloidal Fields, Toroidal Fields and the Mean Flow, Applications to the Boussinesq-Equations, pp. 291–305 in “The Navier-Stokes Equations II — Theory and Numerical Methods”. J.G. Heywood, K. Masuda, R. Rautmann, S.A. Solonnikov, eds., Springer Lecture Notes in Mathematics 1530, 1992.
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Busse, F., Clever, R. (1999). Heteroclinic Cycles and Phase Turbulence. In: Golubitsky, M., Luss, D., Strogatz, S.H. (eds) Pattern Formation in Continuous and Coupled Systems. The IMA Volumes in Mathematics and its Applications, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1558-5_3
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DOI: https://doi.org/10.1007/978-1-4612-1558-5_3
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