Shallow two-component gravity-driven flows with vertical variation
Shallow two-component gravity-driven flows with vertical variation
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DOI：
10.1017/jfm.2012.489
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发表时间：
2013-01
影响因子：
3.7
通讯作者：
J. Kowalski;J. McElwaine
中科院分区：
文献类型：
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作者：
J. Kowalski;J. McElwaine
摘要重力驱动的地球物理质量流通常由非均匀的流固混合物组成。这些成分之间的复杂相互作用导致了雪崩中的侧向堤坝形成，或者泥石流中的颗粒锋面和超额流体孔压等现象。这些影响对于预测跳动和结构上的力是非常重要的，但由于忽略了垂直于主要流动方向的混合物组分的重排，它们只在简化的浅流理论中得到了部分反映。然而，在实际流动中，流变性和有效基础阻力可能很大程度上取决于组分的相对浓度。我们解决了这个问题，并提出了一个浅层混合物的深度平均模型，该模型明确地允许在这个方向上进行重排。特别是，我们考虑了一种流固混合物，它经历了大量的水平运动，以及颗粒的内部沉积和再悬浮，因此类似于泥石流的情况。从一般混合理论出发，导出了颗粒浓度的体积平衡定律和演化方程。深度积分得到了一个由体积质量、深度平均颗粒浓度、颗粒垂直质心和深度平均速度表示的浅层混合流模型。在这个模型中，粒子垂直质心的新方程是通过取粒子质量守恒方程相对于垂直坐标的一阶矩来推导的。我们的方法不进行Boussinesq近似，并导致附加的项将动量通量耦合到垂直质心。该系统是双曲型的，在纯流体或完全混合的齐次极限下可归结为浅水方程。我们强调了沉积对再悬浮的影响，最后给出了一个简单的摩擦反馈，它定性上类似于在瑞士伊尔格拉本获得的大规模实验泥石流数据集。
Abstract Gravity-driven geophysical mass flows often consist of a heterogeneous fluid–solid mixture. The complex interplay between the components leads to phenomena such as lateral levee formation in avalanches, or a granular front and an excess fluid pore pressure in debris flows. These effects are very important for predicting runout and the forces on structures, yet they are only partially represented in simplified shallow flow theories, since rearrangement of the mixture composition perpendicular to the main flow direction is neglected. In realistic flows, however, rheological properties and effective basal drag may depend strongly on the relative concentration of the components. We address this problem and present a depth-averaged model for shallow mixtures that explicitly allows for rearrangement in this direction. In particular we consider a fluid–solid mixture that experiences bulk horizontal motion, as well as internal sedimentation and resuspension of the particles, and therefore resembles the case of a debris flow. Starting from general mixture theory we derive bulk balance laws and an evolution equation for the particle concentration. Depth-integration yields a shallow mixture flow model in terms of bulk mass, depth-averaged particle concentration, the particle vertical centre of mass and the depth-averaged velocity. This new equation in this model for the particle vertical centre of mass is derived by taking the first moment, with respect to the vertical coordinate, of the particle mass conservation equation. Our approach does not make the Boussinesq approximation and results in additional terms coupling the momentum flux to the vertical centre of mass. The system is hyperbolic and reduces to the shallow-water equations in the homogeneous limit of a pure fluid or perfect mixing. We highlight the effects of sedimentation on resuspension and finally present a simple friction feedback which qualitatively resembles a large-scale experimental debris flow data set acquired at the Illgraben, Switzerland.