Quasi-periodic and chaotic flow regimes in a thermally driven, rotating fluid annulus
Quasi-periodic and chaotic flow regimes in a thermally driven, rotating fluid annulus
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热驱动旋转流体环空中的准周期和混沌流态
DOI：
10.1017/s0022112092001836
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发表时间：
1992
影响因子：
3.7
通讯作者：
R. M. Small
中科院分区：
文献类型：
--
作者：
P. Read;M. Bel;D. Johnson;R. M. Small
通过对高普朗特数(Pr=26)流体在水平温度梯度作用下旋转的圆柱形环空中温度和总热量传输的高精度时间序列的分析，给出了结果。重点放在参数空间中接近不规则和/或混沌行为开始的区域。从振荡流到明显的混沌流有两个明显的转变。第一个发生在参数空间的孤立区域，泰勒数从中到高，并伴随着向较低方位波数的转变，其中准周期(m=3)的振幅抖动(在2环面上)让位于很低频率(显然是围绕3环面组织的)的低维(D∼3)混沌调制的抖动。混乱流的空间结构显示出方位向边带的不规则增长和衰减，暗示着相邻方位波数之间的非线性竞争。当稳定性参数Θ减小时，另一个向非周期流动的主要转变发生在较高的泰勒数，这与“结构抖动”的开始有关。这种转变似乎与主要m=3斜压波型内小尺度不稳定性的发展有关，并显示出一条通过间歇性进入混沌的路径。结合确定性混沌的可能机制、仪器的局限性以及以前用低阶谱模型模拟非线性斜压波的尝试，讨论了这两个非周期区域的表观混沌的性质。
Results are presented from analyses of high-precision time series of measurements of temperature and total heat transport obtained in a high-Prandtl-number (Pr = 26) fluid contained in a rotating, cylindrical annulus subject to a horizontal temperature gradient. Emphasis is placed on regions of parameter space close to the onset of irregular and/or chaotic behaviour. Two distinct transitions from oscillatory to apparently chaotic flow have been identified. The first occurs in an isolated region of parameter space at moderate to high Taylor number in association with a transition to a lower azimuthal wavenumber, in which a quasi-periodic (m = 3) amplitude vacillation (on a 2-torus) gives way to a low-dimensional (D ∼ 3) chaotically modulated vacillation at very low frequency (apparently organized about a 3-torus). The spatial structure of the chaotic flow exhibits the irregular growth and decay of azimuthal sidebands suggestive of a nonlinear competition between adjacent azimuthal wavenumbers. The other main transition to aperiodic flow occurs at high Taylor number as the stability parameter Θ is decreased, and is associated with the onset of ‘structural vacillation’. This transition appears to be associated with the development of small-scale instabilities within the main m = 3 baroclinic wave pattern, and exhibits a route to chaos via intermittency. The nature of the apparent chaos in these two aperiodic regimes is discussed in relation to possible mechanisms for deterministic chaos, apparatus limitations, and to previous attempts to model nonlinear baroclinic waves using low-order spectral models.