Charakopoulos A Κ, Karakasidis T E, Papanicolaou P N, Liakopoulos A
Laboratory of Hydromechanics and Environmental Engineering, Department of Civil Engineering, University of Thessaly, 38334 Volos, Greece.
School of Civil Engineering, Department of Water Resources and Environmental Engineering, National Technical University of Athens, 5 Heroon Polytechniou St., 15780 Zografos, Greece.
Chaos. 2014 Jun;24(2):024408. doi: 10.1063/1.4875040.
In the present study, we applied the methodology of the complex network-based time series analysis to experimental temperature time series from a vertical turbulent heated jet. More specifically, we approach the hydrodynamic problem of discriminating time series corresponding to various regions relative to the jet axis, i.e., time series corresponding to regions that are close to the jet axis from time series originating at regions with a different dynamical regime based on the constructed network properties. Applying the transformation phase space method (k nearest neighbors) and also the visibility algorithm, we transformed time series into networks and evaluated the topological properties of the networks such as degree distribution, average path length, diameter, modularity, and clustering coefficient. The results show that the complex network approach allows distinguishing, identifying, and exploring in detail various dynamical regions of the jet flow, and associate it to the corresponding physical behavior. In addition, in order to reject the hypothesis that the studied networks originate from a stochastic process, we generated random network and we compared their statistical properties with that originating from the experimental data. As far as the efficiency of the two methods for network construction is concerned, we conclude that both methodologies lead to network properties that present almost the same qualitative behavior and allow us to reveal the underlying system dynamics.
在本研究中，我们将基于复杂网络的时间序列分析方法应用于垂直湍流加热射流的实验温度时间序列。更具体地说，我们着手解决一个流体动力学问题，即根据构建的网络属性，区分与射流轴相对应的各个区域的时间序列，也就是区分与射流轴附近区域相对应的时间序列和源自具有不同动力学状态区域的时间序列。应用变换相空间方法（k近邻）以及可见性算法，我们将时间序列转换为网络，并评估了网络的拓扑属性，如度分布、平均路径长度、直径、模块化和聚类系数。结果表明，复杂网络方法能够详细区分、识别和探索射流流动的各个动力学区域，并将其与相应的物理行为联系起来。此外，为了否定所研究的网络源自随机过程这一假设，我们生成了随机网络，并将它们的统计属性与源自实验数据的网络的统计属性进行了比较。就两种网络构建方法的效率而言，我们得出的结论是，这两种方法都能得出具有几乎相同定性行为的网络属性，并使我们能够揭示潜在的系统动力学。
