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Updated: May 14, 2026
09:58
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Eulerian field-theoretic closure formalisms for fluid turbulence.
Arjun Berera1, Matthew Salewski, W D McComb
1School of Physics and Astronomy, University of Edinburgh, JCMB, The Kings' Buildings, Edinburgh EH9 3JZ, United Kingdom. ab@ph.ed.ac.uk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 16, 2013
Summary
This study resolves a double-counting issue in the Wyld turbulence theory by introducing an improved method. It demonstrates the equivalence of the Wyld and Martin, Siggia, and Rose formalisms for homogeneous isotropic turbulence (HIT) up to fourth order.
Area of Science:
- Fluid Dynamics
- Statistical Mechanics
- Quantum Field Theory
Background:
- The closure problem in turbulence theory hinders statistical treatments.
- Existing formalisms like Wyld and Martin, Siggia, and Rose (MSR) use quantum field theory techniques.
- The Wyld formalism has a known double-counting issue, with a proposed solution by Lee.
Purpose of the Study:
- To naturally implement Lee's solution within the Wyld formalism, creating an Improved Wyld-Lee Renormalized Perturbation Theory.
- To clarify and compare the Wyld and MSR formalisms.
- To demonstrate the equivalence of the two formalisms for homogeneous isotropic turbulence (HIT).
Main Methods:
- Implementing Lee's ad hoc solution into the Wyld formalism's basic equations.
- Detailed comparison of the procedures and vertex function treatments in Wyld and MSR formalisms.
- Demonstrating formal equivalence up to fourth order.
Main Results:
- A natural implementation of Lee's correction yields the Improved Wyld-Lee Renormalized Perturbation Theory.
- Clarifications reveal that apparent differences in vertex functions stem from procedural variations, not fundamental errors.
- The Wyld and MSR formalisms are shown to be equivalent for HIT up to fourth order.
Conclusions:
- The Improved Wyld-Lee Renormalized Perturbation Theory provides a more integrated solution to the double-counting problem.
- The Wyld and MSR formalisms are reconciled, validating both approaches.
- This work advances the statistical treatment of homogeneous isotropic turbulence.
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