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Intermittency and exponent field dynamics in developed turbulence.
Hirokazu Fujisaka1, Yasuya Nakayama
1Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. fujisaka@i.kyoto-u.ac.jp
Summary
This study explores intermittency dynamics using exponent field fluctuations to characterize energy dissipation. Researchers derived Langevin dynamics from the Navier-Stokes equation, obtaining explicit correlation functions for dissipation rate fluctuations.
Area of Science:
- Fluid dynamics
- Statistical physics
Background:
- Intermittency is a key feature in turbulent flows, characterized by fluctuations in the energy-dissipation rate.
- Understanding the spatiotemporal dynamics of these fluctuations is crucial for developing accurate turbulence models.
Purpose of the Study:
- To phenomenologically construct the probability density for exponent field fluctuations.
- To propose Langevin dynamics for characterizing energy-dissipation rate fluctuations.
- To derive spatiotemporal correlation functions for these fluctuations.
Main Methods:
- Phenomenological construction of probability density for exponent field fluctuations.
- Derivation of Langevin dynamics using the projection-operator method.
- Application of the Navier-Stokes equation as the underlying physical model.
- Gaussian approximation for exponent fluctuations.
Main Results:
- Explicit derivation of spatiotemporal correlation functions for coarse-grained energy-dissipation rate fluctuations.
- Characterization of intermittency dynamics through exponent field fluctuations.
- Successful application of Langevin dynamics to model dissipation rate behavior.
Conclusions:
- The proposed framework effectively describes the spatiotemporal dynamics of intermittency.
- The derived correlation functions provide insights into the statistical properties of energy dissipation.
- This approach offers a valuable tool for analyzing complex fluid phenomena.