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- Title
Analysis of the Quasi Periodic Scenario Leading to Chaos in a Square Cavity.
- Authors
Laouar, S.; Mezaache, E.; Daguenet, M.
- Abstract
Thermal natural convection of air (Pr = 0,71) in a two dimensional square cavity with two vertical walls nonuniformly heated and the two others held adiabatic, is studied numerically. With increasing Rayleigh number (considered here as a control parameter), the system transits to oscillatory regime via a super critical Hopf bifurcation followed by an under critical Hopf bifurcation at critical Rayleigh number of 4,26 × 106. As Rayleigh number increases further a quasi-periodic regime with two frequencies settles. While continuing to increase Rayleigh number, the ratio between the two fundamental frequencies becomes rational. In this case, phase-locking motion is the main regime before chaos. Chaotic state is observed for Rayleigh number greater than 1,4 × 107. The system is sensitive to initial conditions. All numerical results have been characterized by looking to the Poincaré sections and phase portraits. For the chaotic state, the largest Lyapunov exponent is positive and the attractor dimension is fractional.
- Subjects
HEAT transfer; HYDROSTATICS; RAYLEIGH number; DIFFERENTIAL equations; LYAPUNOV exponents; ADIABATIC engines; INTERNAL combustion engines
- Publication
International Review of Physics, 2007, Vol 1, Issue 4, p224
- ISSN
1971-680X
- Publication type
Article