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题名	恒星对流k-ω模型的性质研究
作者	郭志亮
学位类别	硕士
答辩日期	2013-04
授予单位	中国科学院研究生院（云南天文台）
授予地点	北京
导师	李焱
关键词	恒星对流 湍流 k-ω模型
其他题名	Properties of the k-ω Model for Stellar Convection
学位专业	天体物理
中文摘要	在恒星内部，在ε效应或者κ效应和Γ效应的作用下，当满足Schwarzschild判据或者Ledoux判据时，就会引发对流。由于在恒星内部粘性系数很小而对流的尺度很大，导致恒星流体的Reynolds数和Rayleigh很高，使得恒星内部的对流是充分发展的湍流运动。太阳是观测和研究的最详细的一颗恒星，其表面的米粒组织、中米粒组织和超米粒组织是太阳内部对流的直接证据。 在各种各样的对流理论中，广泛使用的是混合长理论和湍对流理论。混合长理论关于平均流体元的假设极大的简化了恒星对流问题，这种等效的方法使得使用混合长理论得出的结果大致与大多数观测相符。然而，混合长理论没有考虑对流超射的影响，也无法考虑湍流的扩散、耗散和各向异性。而湍对流理论建立在流体动力学的坚实基础上，能考虑湍流的扩散、耗散和各向异性，能较好的解决对流超射及其元素混合问题。但是这些湍对流理论都没有考虑对流涡胞的作用，为此Li提出了一个新的恒星对流模型。这个恒星对流模型近似估计了对流涡胞的大小，并提出了对流涡胞内流体运动的平均速度剪切模型。然后它指定了湍流的一个宏观长度模型，得到了k-ε模型在完全局地平衡态下的稳态解，并发展了一个考虑了湍流扩散的k-ω模型。 为了将Li提出的k-ω模型应用到一般的恒星环境中，有必要研究其中模型参数的物理意义，以便限定它们的取值范围。研究表明，模型参数c’μ对湍流的 Péclet数、湍动能、特征时标和特征长度都有影响，除此之外，它还能加快底部对流超射区中湍动能的衰减速率；模型参数c’μ与等效混合长参数α都能增加对流传热效率，它们的对数存在线性关系；模型参数c’μ和底部对流超射区中湍动能的衰减指数θ之间取对数后也存在一个线性关系。
英文摘要	In stellar interior, under the effect of ε effect, κ effect or Γ effect, when the Schwarzschild criterion or the Ledoux criterion stands up, then the convection will develop. Since the small viscosity and large convective length-scale in stellar interior, the Reynolds number and Rayleigh number in stellar fluids are so enormous that stellar convection develops into adequately turbulent flows. The observations and researches of the sun are most detailed in all stars. The granulation, meso-granulation, super-granulation on the solar surface is the direct evidence of solar convection in its interior. Between lots of convection theories, the widely used are the mixing length theory and turbulent convection model theories. The hypothesis of the mean convective element in the mixing length theory greatly simplifies the problem of stellar convection, and the equivalent method makes the results got by the mixing length theory to be consistent with the most of observations. However, the mixing length theory don't take into account the effect of convective overshooting, and it's unable to deal with the turbulent diffusion, dissipation and anisotropy. The turbulent convection model theories, however, which include the turbulent diffusion, dissipation and anisotropy, are builded on the found of fluid dynamics, thus solve the convective overshooting and the corresponding element mixing problem very well. Since the turbulent convection model theories don't take the effect of convective rolling cells into account, Li proposes a new stellar convection model. The new convection model evaluates the size of convective cells approximately, and suggests a average shear model of velocity in the fluids of convective cell. Then it specify a macro-length model of turbulence, and obtains the steady state solutions of k-ε model at fully local equilibrium. Furthermore it develops a k-ω model which includes the effect of turbulent diffusion. To apply the k-ω model into common stellar environments, it's necessary to investigate the physical meanings of model paramters to confine their values. The research states that model parameter c’μ can impact the turbulent flows' Péclet Number, kinetic energy, typical time scale and typical length. Besides, model parameter c’μ can accelerate the rate of damping of the turbulent kinetic energy in the overshooting zone below the base of convection zone. Both model parameter c’μ and equivalent mixing length parameter α can enhance the efficiency of convective heat transfer in the convection zone, further inspection shows that their logarithms can satisfy a linear relation. There is also a linear relation between model parameter c’μ and the damping index θ of turbulent kinetic energy in the convective overshooting zone.
语种	中文
学科主题	天文学
公开日期	2016-05-03
页码	53
内容类型	学位论文
源URL	[http://ir.ynao.ac.cn/handle/114a53/5337]
专题	云南天文台_恒星物理研究组
推荐引用方式 GB/T 7714	郭志亮. 恒星对流k-ω模型的性质研究[D]. 北京. 中国科学院研究生院（云南天文台）. 2013.

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