Key Laboratory of Aero-Acoustics (Beihang University), Ministry of Industry and Information Technology and Key Laboratory of Fluid Mechanics (Beihang University), Ministry of Education, Beijing 100083, People's Republic of China.
Phys Rev E. 2017 Nov;96(5-1):052215. doi: 10.1103/PhysRevE.96.052215. Epub 2017 Nov 20.
The permutation entropy and the statistical complexity are employed to study the boundary-layer transition induced by the surface roughness. The velocity signals measured in the transition process are analyzed with these symbolic quantifiers, as well as the complexity-entropy causality plane, and the chaotic nature of the instability fluctuations is identified. The frequency of the dominant fluctuations has been found according to the time scales corresponding to the extreme values of the symbolic quantifiers. The laminar-turbulent transition process is accompanied by the evolution in the degree of organization of the complex eddy motions, which is also characterized with the growing smaller and flatter circles in the complexity-entropy causality plane. With the help of the permutation entropy and the statistical complexity, the differences between the chaotic fluctuations detected in the experiments and the classical Tollmien-Schlichting wave are shown and discussed. It is also found that the chaotic features of the instability fluctuations can be approximated with a number of regular sine waves superimposed on the fluctuations of the undisturbed laminar boundary layer. This result is related to the physical mechanism in the generation of the instability fluctuations, which is the noise-induced chaos.
排列熵和统计复杂度被用来研究表面粗糙度引起的边界层转捩。在转捩过程中测量的速度信号用这些符号量化器进行分析，以及复杂性-熵因果平面，并确定不稳定性波动的混沌性质。根据符号量化器极值对应的时间尺度，找到了主要波动的频率。层流-湍流转捩过程伴随着复杂涡旋运动组织程度的演变，在复杂性-熵因果平面上也表现为越来越小和平坦的圆圈。借助排列熵和统计复杂度，展示并讨论了实验中检测到的混沌波动与经典 Tollmien-Schlichting 波之间的差异。还发现，不稳定性波动的混沌特征可以用叠加在无扰层流边界层波动上的多个规则正弦波来近似。这一结果与不稳定性波动产生的物理机制有关，即噪声诱导混沌。
