dorsal/arxiv
View SchemaMean Velocity Equation for Turbulent Fluid Flow: An Approach via Classical Statistical Mechanics
| Authors | J. Piest |
|---|---|
| Categories | |
| ArXiv ID | physics/0310054 |
| URL | https://arxiv.org/abs/physics/0310054 |
Abstract
The possibility to derive an equation for the mean velocity field in turbulent flow by using classical statistical mechanics is investigated. An application of projection operator technique available in the literature is used for this purpose. It is argued that the hydrodynamic velocity defined there, in situations where the fluid is turbulent, is to be interpreted as the mean velocity field; in that case, the momentum component of the generalized transport equation derived there is the mean velocity equation. In this paper, stationary incompressible flow for constant mass density and temperature is considered. The stress tensor is obtained as a nonlinear functional of the mean velocity field, the linear part of which is the Stokes tensor. The formula contains a time correlation function in local equilibrium. Presently, there exists a microscopic theory for time correlations in total equilibrium only. For this reason and as a preliminary measure, the formula has been expanded into a power series in the mean velocity; though this limits the applicability to low Reynolds number flow. The second order term has been evaluated in a former paper of the author. For the third order term, the form of the kernel function is derived. Its calculation with the aid of the mode-coupling theory is completed; it will be reported in an separate paper. An numerical application with the data of the circular jet is under way.
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"abstract": "The possibility to derive an equation for the mean velocity field in\nturbulent flow by using classical statistical mechanics is investigated. An\napplication of projection operator technique available in the literature is\nused for this purpose. It is argued that the hydrodynamic velocity defined\nthere, in situations where the fluid is turbulent, is to be interpreted as the\nmean velocity field; in that case, the momentum component of the generalized\ntransport equation derived there is the mean velocity equation. In this paper,\nstationary incompressible flow for constant mass density and temperature is\nconsidered. The stress tensor is obtained as a nonlinear functional of the mean\nvelocity field, the linear part of which is the Stokes tensor. The formula\ncontains a time correlation function in local equilibrium. Presently, there\nexists a microscopic theory for time correlations in total equilibrium only.\nFor this reason and as a preliminary measure, the formula has been expanded\ninto a power series in the mean velocity; though this limits the applicability\nto low Reynolds number flow. The second order term has been evaluated in a\nformer paper of the author. For the third order term, the form of the kernel\nfunction is derived. Its calculation with the aid of the mode-coupling theory\nis completed; it will be reported in an separate paper. An numerical\napplication with the data of the circular jet is under way.",
"arxiv_id": "physics/0310054",
"authors": [
"J. Piest"
],
"categories": [
"physics.class-ph",
"physics.flu-dyn"
],
"title": "Mean Velocity Equation for Turbulent Fluid Flow: An Approach via Classical Statistical Mechanics",
"url": "https://arxiv.org/abs/physics/0310054"
},
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