The long term behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical setup is exposed to an axial magnetic field. The classical Fourier Transform method provides a first estimation of the time dependence of the frequencies associated to the flow, as well as its volume-averaged properties. It is however unable to detect strange attractors close to regular solutions in the Feigenbaum as well as Newhouse–Ruelle–Takens bifurcation scenarios. It is shown that Laskar’s frequency algorithm is sufficiently accurate to identify these strange attractors and thus is an efficient tool for classification of chaotic flows in high dimensional dynamical systems. Our analysis of several chaotic solutions, obtained at different magnetic field strengths, reveals a strong robustness of the main frequency of the flow. This frequency is associated to an azimuthal drift and it is very close to the frequency of the underlying unstable rotating wave. In contrast, the main frequency of volume-averaged properties can vary almost one order of magnitude as the magnetic forcing is decreased. We conclude that, at the moderate differential rotation considered, unstable rotating waves provide a good description of the variation of the main time scale of any flow with respective variations in the magnetic field.

通过时间相关的频率分析研究了混沌流的长期行为。被测系统由导电流体组成，该流体被限制在两个不同旋转的球体之间。球形装置暴露于轴向磁场。经典的傅里叶变换方法提供了与流相关的频率及其体积平均属性的时间依赖性的第一估计。但是，它无法在Feigenbaum以及Newhouse–Ruelle–Takens分叉场景中检测到接近常规解的奇怪吸引子。结果表明，Laskar的频率算法足够准确地识别出这些奇怪的吸引子，因此是一种用于对高维动力系统中的混沌流进行分类的有效工具。我们对在不同磁场强度下获得的几种混沌解的分析表明，流的主频率具有很强的鲁棒性。该频率与方位角漂移相关，并且非常接近下面的不稳定旋转波的频率。相反，随着磁强迫的减小，体积平均特性的主频率可以变化几乎一个数量级。我们得出的结论是，在考虑适度的差动旋转时，不稳定的旋转波很好地描述了任何流的主要时间尺度随磁场的变化而变化的情况。该频率与方位角漂移相关，并且非常接近下面的不稳定旋转波的频率。相反，随着磁强迫的减小，体积平均特性的主频率可以变化几乎一个数量级。我们得出的结论是，在考虑适度的差动旋转时，不稳定的旋转波很好地描述了任何流的主要时间尺度随磁场的变化而变化的情况。该频率与方位角漂移相关，并且非常接近下面的不稳定旋转波的频率。相反，随着磁强迫的减小，体积平均特性的主频率可以变化几乎一个数量级。我们得出的结论是，在考虑适度的差动旋转时，不稳定的旋转波很好地描述了任何流的主要时间尺度随磁场的变化而变化的情况。