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Instantons and the Path to Intermittency in Turbulent Flows.
A Fuchs1, C Herbert2, J Rolland3
1Institute of Physics and ForWind, University of Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany.
Physical Review Letters
|July 29, 2022
Summary
Understanding anomalous fluctuations in turbulent flows, or intermittency, is challenging. This study uses a stochastic Langevin process and entropy-conditioned trajectories to identify optimal paths (instantons) that explain non-Gaussian statistics in turbulent systems.
Area of Science:
- Fluid Dynamics
- Statistical Physics
- Turbulence Research
Background:
- Anomalous fluctuations, known as intermittency, in turbulent flows present a significant challenge to current models.
- Understanding the origins of non-Gaussian statistics at small scales in turbulence is crucial.
Purpose of the Study:
- To model intermittency in turbulent flows using a stochastic Langevin process.
- To identify optimal paths (instantons) governing turbulent cascade trajectories.
- To link these instantons to the emergence of non-Gaussian statistics.
Main Methods:
- Modeling turbulent cascade trajectories as realizations of a stochastic Langevin process with multiplicative noise.
- Conditioning trajectories on their entropy exchange to identify optimal paths (instantons).
- Estimating the effective action from the Langevin equation and measured data.
Main Results:
- Selected entropy-conditioned trajectories concentrate around an optimal path, the instanton.
- The instanton represents the minimum of an effective action derived from the Langevin equation.
- Instantons with negative entropy are identified as key to non-Gaussian statistics at small scales.
Conclusions:
- The Langevin process with multiplicative noise provides a framework for understanding turbulent intermittency.
- Entropy-conditioned instantons offer a new perspective on the emergence of non-Gaussian statistics in turbulence.
- This approach helps pinpoint the specific trajectories responsible for anomalous fluctuations in turbulent flows.
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