{"title":"Investigation of the Local Equilibrium Approximation in a Planar Momentumless Turbulent Wake in a Passively Stratified Fluid","authors":"V. N. Grebenev, A. G. Demenkov, G. G. Chernykh","doi":"10.1134/S1810232824030056","DOIUrl":null,"url":null,"abstract":"<p>The flow in the far planar momentumless turbulent wake in a passively stratified medium is investigated with the use of a mathematical model that includes, along with the averaged equation for transfer of the longitudinal component of velocity, the differential equations for balance of the turbulence energy <span>\\(e\\)</span>, transfer of its dissipation rate <span>\\(\\varepsilon\\)</span>, fluid density defect <span>\\(\\langle\\rho_{1}\\rangle\\)</span>, shear turbulent stress <span>\\(\\langle{u}'{v}'\\rangle\\)</span>, and vertical component of the mass flux vector <span>\\(\\langle v'\\rho'\\rangle\\)</span> in the far wake approximation. Algebraic truncation of the last two equations leads to the known gradient relations for the shear turbulent stress and the vertical component of the mass flux vector. It has been established that with a certain limitation on the values of the empirical constants of the mathematical model and with a time scale growth law consistent with the mathematical model, these relations are joint differential constraints of the model. It has been found that the local equilibrium approximation for the shear turbulent stress is equivalent to the equality to zero of the Poisson bracket for dimensionless values of the turbulent viscosity coefficient and the defect of the longitudinal velocity component. It has been obtained that the local equilibrium approximation for the vertical component of the mass flux vector is equivalent to the equality to zero of the Poisson bracket for dimensionless values of the turbulent diffusion coefficient and mean density. Results of numerical experiments illustrating the theoretical results are presented.</p>","PeriodicalId":627,"journal":{"name":"Journal of Engineering Thermophysics","volume":"33 3","pages":"494 - 506"},"PeriodicalIF":1.3000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Engineering Thermophysics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S1810232824030056","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
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Abstract
The flow in the far planar momentumless turbulent wake in a passively stratified medium is investigated with the use of a mathematical model that includes, along with the averaged equation for transfer of the longitudinal component of velocity, the differential equations for balance of the turbulence energy \(e\), transfer of its dissipation rate \(\varepsilon\), fluid density defect \(\langle\rho_{1}\rangle\), shear turbulent stress \(\langle{u}'{v}'\rangle\), and vertical component of the mass flux vector \(\langle v'\rho'\rangle\) in the far wake approximation. Algebraic truncation of the last two equations leads to the known gradient relations for the shear turbulent stress and the vertical component of the mass flux vector. It has been established that with a certain limitation on the values of the empirical constants of the mathematical model and with a time scale growth law consistent with the mathematical model, these relations are joint differential constraints of the model. It has been found that the local equilibrium approximation for the shear turbulent stress is equivalent to the equality to zero of the Poisson bracket for dimensionless values of the turbulent viscosity coefficient and the defect of the longitudinal velocity component. It has been obtained that the local equilibrium approximation for the vertical component of the mass flux vector is equivalent to the equality to zero of the Poisson bracket for dimensionless values of the turbulent diffusion coefficient and mean density. Results of numerical experiments illustrating the theoretical results are presented.
Abstract The flow in the far planarless momentumulent wake in a passively stratified medium is investigated with the use of a mathematical model that includes, along with the averageaged equation for transfer of longitudinal component of velocity, the differential equations for balance of the turbulence energy \(e\). Transfer of its dissipation rate \(\varepsilon\), fluid density defect \(\langle\rho_{1}\rangle\), shear turbulent stress \(\(e\)、其耗散率的传递、流体密度缺陷、剪切湍流应力、远醒近似的质量通量矢量的垂直分量。通过对后两个方程进行代数截断,可以得到剪切湍流应力和质量通量矢量垂直分量的已知梯度关系。通过对数学模型经验常量值的一定限制以及与数学模型一致的时间尺度增长规律,可以确定这些关系是模型的联合微分约束条件。研究发现,剪切湍流应力的局部平衡近似值等同于湍流粘性系数和纵向速度分量缺陷的无量纲值的泊松括号等于零。对于湍流扩散系数和平均密度的无量纲值,质量通量矢量垂直分量的局部平衡近似等价于泊松括弧等于零。本文介绍了说明理论结果的数值实验结果。
期刊介绍:
Journal of Engineering Thermophysics is an international peer reviewed journal that publishes original articles. The journal welcomes original articles on thermophysics from all countries in the English language. The journal focuses on experimental work, theory, analysis, and computational studies for better understanding of engineering and environmental aspects of thermophysics. The editorial board encourages the authors to submit papers with emphasis on new scientific aspects in experimental and visualization techniques, mathematical models of thermophysical process, energy, and environmental applications. Journal of Engineering Thermophysics covers all subject matter related to thermophysics, including heat and mass transfer, multiphase flow, conduction, radiation, combustion, thermo-gas dynamics, rarefied gas flow, environmental protection in power engineering, and many others.