Bifurcations and Chaos in a Six-dimensional Turbulence Model of Gledzer(Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid mechanics)
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概要
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Gledzer's cascade shell model of turbulence with six real variables is studied numerically using MATHEMATICA 5.1. The Poincare plot of the first mode ν_1 is used to determine periodic, doubly periodic and chaotic solutions and the routes to chaos via both frequency locking and period doubling. The circle map on the torus is well approximated by the summation of several sinusoidal functions. The dependence of the rotation number on the viscosity parameter is in accordance with that of the sine circle map. The complicated bifurcation structure and the revival of a stable periodic solution at a smaller viscosity parameter in the present model indicates that the turbulent state may be very sensitive to the Reynolds number.
- 2006-07-15
著者
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Umeki Makoto
Univ. Tokyo Tokyo
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Umeki Makoto
Department Of Physics Graduate School Of Science University Of Tokyo
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UMEKI Makoto
Department of Physics, Graduate School of Science, University of Tokyo
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