Abstract
Even in simple models the complexity of the flows have restricted theoretical works to either numerical simulation of steady motion or qualitative models involving small number of variables but usually giving successful description of dynamical behaviour. Studies of simpler model systems do suggest that period doubling cascades are a characteristic feature of problems whose dynamics are constrained so that only a few modes can be excited [1]. The presence of these subharmonics bifurcations was observed experimentally for low Pr fluids by Favier et al. [2] under horizontal temperature gradient, and by Gollub and Benson [3] in Rayleigh-Bénard convection.
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References
Knobloch E.K., Moore D.R., Toomre J. and Weiss N.O.,J. Fluid Mech. 166,.409, 1986.
Favier J.J., Rouzaud A. and Cornera J., Rev. Phys. Appl., 22, 713, 1987.
Gollub J.P. and Benson S.V., J. Fluid Mech., 100(3), 449–470, 1980.
Canuto C., Hussaini M.Y., Quarteroni A. and Zang T.A., Spectral Methods in Fluid Dynamics, Springer Series in Comp. Phys., New York, 1987.
Byrne G.D. and Hindmarsh A.C., J. Comp. Phys., 70, 1, 1987.
Randriamampianina A., Bontoux P. and Roux B., Intl. J. Heat Mass Transfer, 30, 1275, 1987.
Pulicani J.P., Crespo del Arco E., Randriamampianina A., Bontoux P. and Peyret R., Spectral Simulations of Oscillatory Convection at Low Prandtl Number, in Print in Intl. J. Numer. Meth. Fluids, 1988.
Crespo del Arco E., Peyret R., Pulicani J.P. and Randriamampianina A., Spectral Calculations of Oscillatory Convective Flows, in Finite Element Analysis, T.J. Chung & G.R. Karr Eds., UAH Press, Huntsville, Alabama, 1464–1472, 1989.
Crespo del Arco E., Randriamampianina A. and Bontoux P., Two-Dimensional Simulation of Time-Dependent Convective Flow of a Pr→0 Fluid. A Period Doubling Transition to Chaos, in Synergetics, Order & Chaos, M.G. Velarde Ed., World Scientific, 244–257, 1988.
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© 1990 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Randriamampianina, A., Crespo Del Arco, E., Fontaine, J.P., Bontoux, P. (1990). Spectral Method for Two-Dimensional Time-Dependent Pr→0 Convection. In: Roux, B. (eds) Numerical Simulation of Oscillatory Convection on Low-Pr Fluids. Notes on Numerical Fluid Mechanics (NNFM), vol 27. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87877-9_30
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DOI: https://doi.org/10.1007/978-3-322-87877-9_30
Publisher Name: Vieweg+Teubner Verlag
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