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Improved epsilon expansion for three-dimensional turbulence: two-loop renormalization near two dimensions.
L Ts Adzhemyan1, J Honkonen, M V Kompaniets
1Department of Theoretical Physics, St. Petersburg University, Russia.
Summary
This study improves the epsilon expansion for stochastic turbulence theory by addressing pole singularities near two dimensions. A new renormalization method yields consistent results and better agreement with experimental data for the Kolmogorov constant.
Area of Science:
- Fluid Dynamics
- Statistical Physics
- Quantum Field Theory
Background:
- The epsilon expansion is a key tool in the stochastic theory of turbulence.
- Pole singularities near d=2 dimensions pose challenges for existing models.
- Accurate calculation of universal quantities requires careful renormalization.
Purpose of the Study:
- To construct an improved epsilon expansion at two-loop order.
- To incorporate the effects of pole singularities at d-->2.
- To resolve contradictions in existing renormalization approaches.
Main Methods:
- Analysis of two different renormalization approaches for the random force correlation function.
- Two-loop calculations using a modified renormalization scheme.
- Incorporation of partial resummation of pole singularities.
Main Results:
- The approach using only nonlocal correlation function renormalization leads to contradictions.
- A renormalization scheme with an added local term yields consistent two-loop results.
- The improved method significantly enhances agreement with experimental Kolmogorov constant values.
Conclusions:
- A consistent two-loop renormalization scheme is established for stochastic turbulence.
- The improved epsilon expansion accurately captures singularity effects near d=2.
- This work advances the predictive power of turbulence theory for experimental validation.