Extreme events and instantons in Lagrangian passive scalar turbulence models.
Extreme events and instantons in Lagrangian passive scalar turbulence models.
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DOI：
10.1103/physreve.106.015101
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
Mnerh Alqahtani;L. Grigorio;T. Grafke
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文献类型：
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作者：
Mnerh Alqahtani;L. Grigorio;T. Grafke
流体中标量的平流和混合是工程和自然科学中的一个重要问题。被动标量的统计表现出复杂的行为，即使在高斯速度场的存在。本文讨论了两种拉格朗日湍流模型，它们是在现有的流体变形模型的基础上，增加了一个均匀梯度的被动标量场。在一定的雷诺数范围内，这些模型可以再现被动标量湍流的统计特性。对于这些模型，我们演示了如何通过计算瞬子来恢复极端被动标量梯度事件，即，相关随机场理论的鞍点结构。它使我们既能再现与被动标量湍流相关的重尾统计，又能恢复导致这种极端事件的最可能机制。我们进一步证明了这些模型中的大负应变事件发生自发对称破缺。
The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. The statistics of the passive scalar exhibit complex behavior even in the presence of a Gaussian velocity field. This paper is concerned with two Lagrangian turbulence models that are based on the recent fluid deformation model, but adding a passive scalar field with uniform mean gradient. For a range of Reynolds numbers, these models can reproduce the statistics of passive scalar turbulence. For these models, we demonstrate how events of extreme passive scalar gradients can be recovered by computing the instanton, i.e., the saddle-point configuration of the associated stochastic field theory. It allows us to both reproduce the heavy-tailed statistics associated with passive scalar turbulence, and recover the most likely mechanism leading to such extreme events. We further demonstrate that events of large negative strain in these models undergo spontaneous symmetry breaking.