How to define the boundaries of a convective zone, and how extended is overshooting ?
How to define the boundaries of a convective zone, and how extended is overshooting ?
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DOI：
10.1111/j.1365-2966.2008.12969.x
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发表时间：
2007-07
影响因子：
4.8
通讯作者：
L. Deng;D. Xiong
中科院分区：
文献类型：
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作者：
L. Deng;D. Xiong
在非局部对流理论中，对流是无限延伸的，因此不能像局部理论那样清楚地定义表观边界。从局部模型和非局部模型的相似结构具有相同的对流区深度的要求出发，考虑到湍流对流的驱动机制，我们认为对流区边界的正确定义应该是对流能通量（即湍流速度和温度的相关性）改变其符号的地方。因此，当通量为正时，它是一个对流不稳定区，当通量为负时，它是一个对流过冲区。通常的非局部混合长度理论所描绘的过冲区的物理图像是不正确的。事实上，对流在到达不稳定边界之前很久就已经是亚绝热的（del < del（ad）），而在对流区下面的过冲区，对流是亚绝热和超辐射的（del（rad）< del < del（ad））。绝热和辐射温度梯度之间的过渡是连续和平滑的，而不是突然切换。在不稳定区中，温度梯度接近辐射温度梯度而不是绝热温度梯度。我们要再次指出，对于不同的物理量，过冲距离是不同的。在恒星内部深处的过冲区，湍流速度和温度的e-折叠长度约为0.3H（P），而速度-温度相关的e-折叠长度则短得多，约为0.09H（P）。在恒星演化的背景下，通过恒星物质混合的程度来衡量的超调距离应该更大。根据演化时间尺度的不同，估计其大小可达0.25-1.7H（P）。超调距离越大，时间尺度越长。这是因为在混合过程中的扩展过冲尾部的参与。
In non-local convection theory, convection extends without limit and therefore an apparent boundary cannot be defined clearly, as in local theory. From the requirement that a similar structure for both local and non-local models has the same depth of convection zone, and taking into account the driving mechanism of turbulent convection, we argue that a proper definition of the boundary of a convective zone should be the place where the convective energy flux (i.e. the correlation of turbulent velocity and temperature) changes its sign. Therefore, it is a convectively unstable region when the flux is positive, and it is a convective overshooting zone when the flux becomes negative. The physical picture of the overshooting zone drawn by the usual non-local mixing-length theory is incorrect. In fact, convection is already subadiabatic (del < del(ad)) long before reaching the unstable boundary, while in the overshooting zone below the convective zone, convection is subadiabatic and superradiative (del(rad) < del < del(ad)). The transition between the adiabatic and radiative temperature gradients is continuous and smooth instead of being a sudden switch. In the unstable zone, the temperature gradient approaches a radiative temperature gradient rather than an adiabatic temperature gradient. We would like to note again that the overshooting distance is different for different physical quantities. In an overshooting zone at deep stellar interiors, the e-folding lengths of turbulent velocity and temperature are about 0.3H(P), whereas that of the velocity-temperature correlation is much shorter, about 0.09H(P). The overshooting distance in the context of stellar evolution, measured by the extent of the mixing of stellar matter, should be more extended. It is estimated to be as large as 0.25-1.7H(P) depending on the evolutionary time-scale. The larger the overshooting distance, the longer the time-scales. This is because of the participation of the extended overshooting tail in the mixing process.