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| Variational approach to the closure problem of turbulence theory | |
Qian J
| |
| Source Publication | Physics of Fluids
 |
| 1983 | |
| Volume | 26Issue:8Pages:2098-2104 |
| ISSN | 1070-6631 |
| Abstract | A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963). |
| Keyword | Closure Law Kolmogoroff Theory Turbulent Flow Variational Principles Damping Fokker-planck Equation Liouville Equations Statistical Mechanics |
| DOI | 10.1063/1.864414 |
| Indexed By | SCI |
| Language | 英语 |
| WOS ID | WOS:A1983RD25000009 |
| WOS Research Area | Mechanics ; Physics |
| WOS Subject | Mechanics ; Physics, Fluids & Plasmas |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/39908 |
| Collection | 力学所知识产出(1956-2008) |
| Recommended Citation GB/T 7714 | Qian J. Variational approach to the closure problem of turbulence theory[J]. Physics of Fluids,1983,26,8,:2098-2104. |
| APA | Qian J.(1983).Variational approach to the closure problem of turbulence theory.Physics of Fluids,26(8),2098-2104. |
| MLA | Qian J."Variational approach to the closure problem of turbulence theory".Physics of Fluids 26.8(1983):2098-2104. |
| Files in This Item: | Download All | |||||
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| A470.pdf（533KB） | 开放获取 | -- | View Download | |||
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