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Detecting the chaotic nature in a transitional boundary layer using symbolic information-theory quantifiers.
Wen Zhang1, Peiqing Liu1, Hao Guo1
1Key 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.
Physical Review. E
|January 20, 2018
Summary
Surface roughness triggers boundary-layer transition, identified as chaotic fluctuations using permutation entropy and statistical complexity. These methods reveal insights into instability generation and differentiate chaotic signals from classical waves.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Chaos theory
Background:
- Surface roughness is a key factor influencing boundary-layer transition in fluid flows.
- Understanding the transition from laminar to turbulent flow is crucial for aerodynamic and hydrodynamic applications.
- Symbolic analysis methods offer novel ways to characterize complex dynamical systems.
Purpose of the Study:
- To investigate the boundary-layer transition induced by surface roughness using symbolic quantifiers.
- To identify the chaotic nature of instability fluctuations during the transition process.
- To differentiate experimentally observed chaotic fluctuations from classical Tollmien-Schlichting waves.
Main Methods:
- Analysis of velocity signals using permutation entropy and statistical complexity.
- Application of the complexity-entropy causality plane for dynamical system characterization.
- Determination of dominant fluctuation frequencies from symbolic quantifier time scales.
Main Results:
- The chaotic nature of instability fluctuations during boundary-layer transition was identified.
- Dominant fluctuation frequencies were determined via symbolic quantifier time scales.
- The complexity-entropy causality plane showed evolving organization of eddy motions.
- Chaotic fluctuations were distinguished from Tollmien-Schlichting waves.
- Chaotic features were approximated by superimposed sine waves, indicating noise-induced chaos.
Conclusions:
- Permutation entropy and statistical complexity are effective tools for analyzing boundary-layer transition.
- Surface roughness induces chaotic instability fluctuations, distinct from classical wave phenomena.
- The findings provide insights into the physical mechanisms of noise-induced chaos in boundary layers.
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