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Energy and Entropy in Turbulence Decompositions
Václav Uruba1,2
1Department of Fluid Dynamics, Institute of Thermomechanics of the Czech Academy of Sciences (CAS), v. v. i., Dolejškova 5, 18200 Praha 8, Czech Republic.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study clarifies energy and entropy roles in turbulent flow decomposition using proper orthogonal decomposition (POD) and bi-orthogonal decomposition (BOD). New mode definitions enhance physical interpretation and reduced-order modeling (ROM) strategies.
Area of Science:
- Fluid Dynamics
- Turbulence Research
- Data Analysis
Background:
- Turbulent velocity flow-field decomposition is crucial for understanding complex fluid dynamics.
- Existing methods like proper orthogonal decomposition (POD) and bi-orthogonal decomposition (BOD) offer insights but can be difficult to interpret.
- Variations in decomposition methods and result interpretation pose challenges in fluid dynamics research.
Purpose of the Study:
- To elucidate the roles of energy and entropy in decomposing turbulent velocity flow-fields.
- To propose specific definitions for decomposition modes to improve clarity.
- To present energy- and entropy-motivated perspectives on decomposed modes for enhanced physical interpretation.
Main Methods:
- Utilizing energy-based decomposition techniques, specifically proper orthogonal decomposition (POD) and bi-orthogonal decomposition (BOD).
- Developing and specifying novel definitions for decomposition modes.
- Applying energy and entropy concepts to analyze the decomposed modes.
Main Results:
- The paper clarifies the roles of energy and entropy in the decomposition of turbulent velocity flow-fields.
- Novel mode definitions are presented, aiding in clearer interpretation of decomposition results.
- Energy- and entropy-motivated views provide new avenues for understanding decomposed modes.
Conclusions:
- The proposed energy- and entropy-based approach enhances the physical interpretation of modes in turbulent flow analysis.
- This framework offers potential improvements for reduced-order modeling (ROM) strategy efficiency.
- The study provides a clearer understanding of decomposition methods in fluid dynamics.
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