Segregation-induced finger formation in granular free-surface flows
Segregation-induced finger formation in granular free-surface flows
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DOI：
10.1017/jfm.2016.673
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发表时间：
2016-11
影响因子：
3.7
通讯作者：
J. L. Baker;C. G. Johnson;J. Gray
中科院分区：
文献类型：
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作者：
J. L. Baker;C. G. Johnson;J. Gray
地球物理颗粒流，如滑坡、火山碎屑流和雪崩，由具有不同表面粗糙度或形状的颗粒组成，由于尺寸差异，这些颗粒在流动过程中有分离的趋势。这种偏析导致了具有不同摩擦特性的区域的形成，这些区域反过来又可以反馈到整体流动中。本文针对这些分离-迁移反馈效应引入了一个定态良好的深度平均模型。通过假设细粒以上大颗粒的反梯度层和Bagnold剪切剖面，将致密颗粒流的完整偏析方程整合到雪崩厚度中。由此产生的大颗粒输运方程随后与质量和动量守恒的深度平均方程耦合，并通过与成分相关的基本摩擦定律产生反馈，这意味着在有更多大颗粒的地方会产生更大的摩擦。新的方程组包括动量平衡中的粘性项，这些项来自于致密颗粒流的$\unicode[STIX]{x1D707}(I)$ -流变学，代表了对先前模型的奇异摄动。稳定均匀基态的线性稳定性计算证明了这些高阶项的重要性，它们确保了，与无粘方程不同，增长率在任何地方都是有界的。因此，这个新系统在数学上是很好的。双分散物质沿斜面向下传播的二维模拟显示了一个不稳定的富含大量物质的流动锋的发展，它随后破裂成一系列手指状结构，每个结构都由粗粒度的横向堤防包围。手指的关键属性与网格分辨率无关，由物理粘度控制。在室内实验中观察到这种分离诱导的指状形成过程，数值计算结果与定性结果一致。
Geophysical granular flows, such as landslides, pyroclastic flows and snow avalanches, consist of particles with varying surface roughnesses or shapes that have a tendency to segregate during flow due to size differences. Such segregation leads to the formation of regions with different frictional properties, which in turn can feed back on the bulk flow. This paper introduces a well-posed depth-averaged model for these segregation-mobility feedback effects. The full segregation equation for dense granular flows is integrated through the avalanche thickness by assuming inversely graded layers with large particles above fines, and a Bagnold shear profile. The resulting large particle transport equation is then coupled to depth-averaged equations for conservation of mass and momentum, with the feedback arising through a basal friction law that is composition dependent, implying greater friction where there are more large particles. The new system of equations includes viscous terms in the momentum balance, which are derived from the $\unicode[STIX]{x1D707}(I)$ -rheology for dense granular flows and represent a singular perturbation to previous models. Linear stability calculations of the steady uniform base state demonstrate the significance of these higher-order terms, which ensure that, unlike the inviscid equations, the growth rates remain bounded everywhere. The new system is therefore mathematically well posed. Two-dimensional simulations of bidisperse material propagating down an inclined plane show the development of an unstable large-rich flow front, which subsequently breaks into a series of finger-like structures, each bounded by coarse-grained lateral levees. The key properties of the fingers are independent of the grid resolution and are controlled by the physical viscosity. This process of segregation-induced finger formation is observed in laboratory experiments, and numerical computations are in qualitative agreement.