Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. II. Limitations of Local Models
Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. II. Limitations of Local Models
复制标题
扩散分层剪切流的湍流传输：从局部模型到全局模型。
DOI：
10.3847/1538-4357/aacd15
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
P. Garaud
中科院分区：
文献类型：
--
作者：
D. Gagnier;P. Garaud
本文继续本系列第一部分开始的扩散剪切不稳定性的系统研究。在这项工作中，我们主要集中在量化的非本地混合，这是不考虑在扎恩的混合模型的影响。我们提出了一个新的模型设置，旨在包含共存的层流和湍流剪切层的直接数值模拟的结果。与第一部分一样，我们使用Lignières的低Péclet数近似来模拟扰动的演化。我们的主要发现有两个方面。首先，只要满足Zahn的非线性准则JPr <（JPr）c，就不一定会产生湍流，其中J = N2/S2是局部梯度Richardson数，Pr = ν/κT是普朗特数，并且（JPr）c ≥ 0.007。我们已经证明，在这个极限中，湍流混合的存在或不存在滞后地取决于剪切层的历史。第二，Zahn的非线性不稳定性判据仅近似地定位于湍流层的边缘，并且在JPr <（JPr）c的区域之外的混合也可以以类似于对流过冲的方式发生。我们发现，湍流动能在剪切不稳定区的边缘外大致呈指数衰减，其长度尺度δ与湍流涡旋的尺度成正比，而湍流涡旋的尺度本身是赞恩尺度的量级（见第一部分）。我们的研究结果表明，混合扩散剪切不稳定性应建模更小心比目前标准的恒星演化代码。
This paper continues the systematic investigation of diffusive shear instabilities initiated in Part I of this series. In this work, we primarily focus on quantifying the impact of nonlocal mixing, which is not taken into account in Zahn’s mixing model. We present the results of direct numerical simulations in a new model setup designed to contain coexisting laminar and turbulent shear layers. As in Part I, we use the low Péclet number approximation of Lignières to model the evolution of the perturbations. Our main findings are twofold. First, turbulence is not necessarily generated whenever Zahn’s nonlinear criterion JPr < (JPr)c is satisfied, where J = N2/S2 is the local gradient Richardson number, Pr = ν/κT is the Prandtl number, and (JPr)c ≃ 0.007. We have demonstrated that the presence or absence of turbulent mixing in this limit hysteretically depends on the history of the shear layer. Second, Zahn’s nonlinear instability criterion only approximately locates the edge of the turbulent layer, and mixing beyond the region where JPr < (JPr)c can also take place in a manner analogous to convective overshoot. We found that the turbulent kinetic energy decays roughly exponentially beyond the edge of the shear-unstable region, on a lengthscale δ that is directly proportional to the scale of the turbulent eddies, which are themselves of the order of the Zahn scale (see Part I). Our results suggest that mixing by diffusive shear instabilities should be modeled with more care than is currently standard in stellar evolution codes.