On the Hopf bifurcation occurring in the two‐layer Rayleigh–Be´nard convective instability
作者:
P. Colinet,
J. C. Legros,
期刊:
Physics of Fluids
(AIP Available online 1994)
卷期:
Volume 6,
issue 8
页码: 2631-2639
ISSN:1070-6631
年代: 1994
DOI:10.1063/1.868153
出版商: AIP
数据来源: AIP
摘要:
The oscillating convective structures appearing at the threshold of the two‐layer Rayleigh–Be´nard instability are analyzed in the nonlinear regime. By deriving the amplitude equations for left‐ and right‐traveling waves from the infinite Prandtl number Boussinesq equations, it is shown that one of these waves should generally appear, rather than standing waves, in sufficiently large cells. Numerical results show that these waves have a limited range of existence, because a hysteretic transition to stationary convection occurs when the Rayleigh number is increased (via approach of a heteroclinic orbit for standing waves, and steady‐state bifurcation for traveling waves). From numerical evidence and by comparison with similar behaviors encountered in the one‐layer two‐component problem, it is inferred that the overall behavior is typical of a codimension‐2 Takens–Bogdanov bifurcation.
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