A nonlinear approach to transition in subcritical plasmas with sheared flow
A nonlinear approach to transition in subcritical plasmas with sheared flow
复制标题
DOI：
10.1063/1.4999848
复制
发表时间：
2017-08
期刊：
影响因子：
--
通讯作者：
C. Pringle;B. McMillan;B. Teaca
中科院分区：
文献类型：
--
作者：
C. Pringle;B. McMillan;B. Teaca
在许多等离子体系统中，引入小的背景剪切流足以线性地稳定系统。与平均线性增长率相比，非线性动力学对剪切流的敏感性要小得多，并且非常小的振幅扰动可以导致持续的湍流。我们探讨的一般性问题，如何以及何时从近层流状态的过渡到持续的湍流发生的互换不稳定性的模型被用作一个具体的例子。这些问题基本上是非线性的，答案必须超越小扰动的线性瞬态放大。两种方法，占非线性相互作用，因此，在这里探讨。探索的第一种方法是边缘跟踪，它确定了层流和湍流状态的吸引盆地之间的边界。在这里，边缘被发现是围绕一个精确的，本地化的，行波解的结构，一个解决方案，是定性类似于雪崩般的爆发中看到的湍流制度。第二种方法是应用非线性，非模态稳定性理论，使我们能够识别最小的干扰，可以触发湍流（最小种子的问题），因此，以量化如何稳定的层流政权。从这些完全非线性的方法得到的结果提供了信心的最小种子的半解析近似的推导。
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution; a solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provides confidence in the derivation of a semi-analytic approximation for the minimal seed.