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外文期刊>The Astrophysical journal
>Turbulence in Stars. III. Unified Treatment of Diffusion, Convection, Semiconvection, Salt Fingers, and Differential Rotation
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Turbulence in Stars. III. Unified Treatment of Diffusion, Convection, Semiconvection, Salt Fingers, and Differential Rotation
The goal of this paper is to propose a unified treatment of diffusion, convection, semiconvection, salt fingers, overshooting, and rotational mixing. The detection of SN 1987A has served, among other things, to highlight the incompleteness of our understanding of such phenomena. Moreover, the variety of solutions proposed thus far to deal with each phenomenon separately, the uncertainty about the Ledoux-Schwarzschild criteria, the extent of overshooting, the effect of a μ gradient, the role of differential rotational mixing, etc., have added further urgency to the need of a unified, rather than a case-by-case, treatment of these processes. Since at the root of these difficulties lies the fact that we are dealing with a highly nonlinear, turbulent regime under the action of three gradients T (temperature), C (concentration), and (mean flow), it is not surprising that such difficulties have arisen. In this paper we propose a unified treatment based on a turbulence model. A key difference with previous models is that we do not employ heuristic arguments to determine the five basic timescales that enter the problem and that entail a corresponding number of adjustable constants. These timescales are computed using renormalization group (RNG) techniques. The model comes in three flavors: (a) all the turbulent variables are treated nonlocally; (b) the turbulent kinetic energy K and its rate of dissipation are nonlocal, while the remaining turbulence variables (fluxes, Reynolds stresses, etc.) are treated locally; and (c) all turbulence variables are local. In the latter case, one must specify a mixing length. Some of the results are as follows: 1. The local model entails the solution of two algebraic equations, one being the flux conservation law. By solving them, we obtain the desired - ad versus μ relations for semiconvection and salt fingers. We also derive other variables of interest, turbulent diffusivities, Peclet number, turbulent velocity, etc. 2. Schwarzschild and Ledoux criteria for instability are replaced by a new criterion that is physically equivalent to the requirement that turbulent mixing can exist only so long as the turbulent kinetic energy is positive. In addition to , ad, and μ, the new criterion depends on the turbulent diffusivities for temperature and concentration that only a turbulence model can provide. 3. We derive the dynamic equations necessary to quantify the extent of overshooting OV in the presence of a μ barrier. 4. We prove that OV(μ) OV(μ = const.). Although this result is physically understandable, no direct proof has been available as yet. 5. We derive the turbulent diffusivity for a passive scalar, one that does not affect a preexisting turbulence, e.g., a sedimentation of He. We show that it differs from that of an active scalar, e.g., a μ field causing semiconvection and/or salt fingers. Such diffusivity is a function of the temperature gradient (stable/unstable) and shear (rotational mixing). 6. We show that the turbulent diffusivities of momentum (entering the angular momentum equation), of heat (entering the model of convection), and concentration (entering the diffusion equation and/or semiconvection and salt fingers) are different from one another and should not be taken to be the same, as has been done thus far. 7. We consider the effect of shear. We solve the local turbulence problem analytically and derive the turbulent diffusivities for momentum, heat, and concentration in terms of the three gradients of the mean fields, T, C, and . Since shear is itself a source of turbulent mixing, one could expect it to enhance the diffusivities. However, its interaction with salt fingers and semiconvection is a subtle one, and the opposite may occur, a phenomenon for which we offer a physical interpretation and a validation with laboratory data. 8. A comparison is made with previous models.
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机译：本文的目的是提出对扩散，对流，半对流，盐指，超调和旋转混合的统一处理。 SN 1987A的发现除其他外，突出了我们对这种现象的理解的不完整。此外，迄今为止提出的各种解决方案分别解决每种现象，有关Ledoux-Schwarzschild准则的不确定性，超调的程度，μ梯度的影响，差分旋转混合的作用等进一步增加了迫切需要对这些过程进行统一而不是逐案处理。由于这些困难的根源在于我们在三个梯度T（温度），C（浓度）和（平均流量）的作用下处理高度非线性的湍流状态，因此难怪这些困难已经出现。在本文中，我们提出了基于湍流模型的统一处理。与以前的模型的主要区别在于，我们不使用启发式参数来确定进入问题的五个基本时标，而是需要相应数量的可调常数。使用重新归一化组（RNG）技术计算这些时间尺度。该模型具有三种风格：（a）所有湍流变量都被非局部处理; （b）湍动能K及其耗散率不是局部的，而其余的湍流变量（通量，雷诺应力等）则是局部处理的; （c）所有湍流变量都是局部的。在后一种情况下，必须指定混合长度。一些结果如下：1.局部模型需要两个代数方程的解，一个是通量守恒定律。通过求解它们，我们获得了半对流和盐指的理想-ad与μ关系。我们还得出其他感兴趣的变量，湍流扩散率，Peclet数，湍流速度等。2. Schwarzschild和Ledoux的不稳定性标准由新的标准代替，该新的标准在物理上等同于只有在混合条件下才能存在湍流混合的要求。湍动能为正。除了，ad和μ之外，新标准还取决于仅湍流模型可以提供的温度和浓度的湍流扩散率。 3.我们导出了在存在μ势垒时量化过冲OV程度所必需的动力学方程。 4.我们证明OV（μ）展开▼
