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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Characterizing Small-Scale Dynamics of Navier-Stokes Turbulence with Transverse Lyapunov Exponents: A Data
Masanobu Inubushi1,2, Yoshitaka Saiki3, Miki U Kobayashi4
1Department of Applied Mathematics, Tokyo University of Science, Tokyo 162-8601, Japan.
Physical Review Letters
|January 5, 2024
Summary
Data assimilation of turbulence reconstructs small-scale structures from large-scale data. A new framework using transverse Lyapunov exponents reveals a critical length scale for successful turbulence data assimilation.
Area of Science:
- Fluid Dynamics
- Chaos Theory
- Data Assimilation
Background:
- Data assimilation (DA) is vital for turbulence forecasting and understanding.
- Reconstructing small-scale turbulent structures from large-scale data is a key challenge.
Purpose of the Study:
- To develop a theoretical framework for turbulence data assimilation.
- To identify key conditions for effective data assimilation in turbulent flows.
Main Methods:
- Utilizing transverse Lyapunov exponents (TLEs) from synchronization theory.
- Performing stability analysis based on TLEs.
- Relating maximal Lyapunov exponents to TLEs.
Main Results:
- Identified a critical length scale essential for turbulence data assimilation.
- Demonstrated that turbulent dynamics smaller than this scale synchronize with larger scales.
- Clarified the dependence of this critical length scale on the Reynolds number.
Conclusions:
- The proposed framework provides a theoretical basis for turbulence data assimilation.
- The critical length scale is a fundamental parameter governing the success of DA.
- Reynolds number significantly influences the predictability of small-scale turbulence via DA.
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