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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Lagrangian finite-time fluctuation relation in isotropic turbulence
Hanxun Yao1, Tamer Zaki1, Charles Meneveau1
1Department of Mechanical Engineering, Johns Hopkins University , Baltimore, MD, USA.
Summary
The fluctuation relation (FR) in non-equilibrium thermodynamics is confirmed for isotropic turbulence, showing exponential behavior in entropy generation rates. This holds true under Lagrangian analysis, but not in Eulerian frameworks.
Area of Science:
- Thermodynamics
- Fluid Mechanics
- Statistical Physics
Background:
- Entropy generation rate in turbulence is linked to the energy cascade rate via the Kolmogorov-Hill equation.
- The fluctuation relation (FR) from non-equilibrium thermodynamics predicts exponential behavior for entropy production rate ratios.
- Prior work confirmed FR under specific limiting assumptions.
Purpose of the Study:
- To examine the applicability of the fluctuation relation (FR) to isotropic turbulence under less stringent assumptions.
- To analyze entropy generation rates averaged over various time intervals relative to eddy turnover times.
Main Methods:
- Analysis of time-resolved data for isotropic turbulence at a Taylor-scale Reynolds number (Reλ=433).
- Entropy generation rates were averaged over intervals from one to several eddy turnover times.
- Comparison of FR validity using Lagrangian (along fluid trajectories) and Eulerian (fixed positions) frameworks.
Main Results:
- The fluctuation relation (FR) was found to be valid for isotropic turbulence, exhibiting near-exponential behavior for probability ratios of positive and negative entropy generation.
- FR-consistent results were obtained using finite-time averaging within a Lagrangian framework with filtered convective velocities.
- The FR did not hold when time-averaging was performed at fixed Eulerian positions.
Conclusions:
- The study confirms the validity of the fluctuation relation in isotropic turbulence under relaxed assumptions.
- Lagrangian finite-time averaging is crucial for observing FR-consistent behavior in turbulent entropy generation.
- The findings support the use of the scale-integrated Kolmogorov-Hill equation to describe turbulent cascade processes consistent with non-equilibrium thermodynamics.
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