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Updated: Jun 25, 2026
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Published on: June 24, 2013
One-point velocity statistics in decaying homogeneous isotropic turbulence
12-24-6-101 Honmachi, Fuchu, Tokyo 183-0027, Japan.
Summary
Researchers achieved a closure for the Monin-Lundgren hierarchy, simplifying equations for turbulent velocity distributions. This leads to a two-parameter family of Gaussian solutions for decaying homogeneous isotropic turbulence.
Area of Science:
- Fluid Dynamics
- Turbulence Modeling
- Statistical Mechanics
Background:
- The Monin-Lundgren hierarchy describes the evolution of velocity statistics in turbulent flows.
- Accurate modeling of decaying homogeneous isotropic turbulence is crucial for understanding complex fluid phenomena.
- Previous approaches faced challenges in closing the hierarchy for multi-point velocity distributions.
Purpose of the Study:
- To develop a closure for the Monin-Lundgren hierarchy.
- To derive the one-point velocity distribution for decaying homogeneous isotropic turbulence.
- To identify the resulting solution family.
Main Methods:
- Applied a closure approximation to the Monin-Lundgren hierarchy.
- Focused on the first equation governing the one-point velocity distribution.
- Analyzed the mathematical properties of the resulting system.
Main Results:
- Achieved a reasonable closure for the hierarchy.
- Derived a two-parameter family of solutions for the one-point velocity distribution.
- Identified these solutions as Gaussian distributions.
Conclusions:
- The closure method provides a tractable approach to studying turbulent velocity statistics.
- The derived Gaussian solutions offer a simplified yet informative model for decaying turbulence.
- This work contributes to a better theoretical understanding of turbulent flow behavior.
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