标题： 稳定密集浅层颗粒流中的表面曲率和次级涡旋 显示英文标题

标题： Surface curvature and secondary vortices in steady dense shallow granular flows

摘要： 密集颗粒流由于法向应力差的存在，表现出表面变形和次级流动。 然而，对这两个特征的完整数学建模仍然缺乏。 本文研究了一种在任意截面倾斜渠道中稳定浅层密集流动，通过基于流动浅度的展开结合二阶颗粒流变学推导出渐近解。 主导阶流动是单轴的，沿流向的速度对应于由变化的流动深度缩放的Bagnold剖面的横向并置。 一阶修正引入了与主流动方向垂直平面内的两个反向旋转的涡旋（中心下沉），以及自由表面的向上弯曲。 这些解与DEM模拟进行了比较，它们在定量上相符。 然后，这一结果结合实验室实验，用于推断密集干颗粒流中的第二个法向应力差的测量值。 显示英文摘要

摘要： Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady shallow dense flow down an inclined channel of arbitrary cross-section, for which asymptotic solutions are derived by using an expansion based on the flow shallowness combined with a second-order granular rheology. The leading order flow is uniaxial, with a streamwise velocity corresponding to a lateral juxtaposition of Bagnold profiles scaled by the varying flow depth. The correction at first order introduces two counter-rotating vortices in the plane perpendicular to the main flow direction (with downwelling in the centre), and an upward curve of the free surface. These solutions are compared to DEM simulations, which they match quantitatively. This result is then used together with laboratory experiments to infer measurements of the second-normal stress difference in dense dry granular flow.