Granular column collapses down rough, inclined channels
Granular column collapses down rough, inclined channels
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DOI：
10.1017/jfm.2011.21
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发表时间：
2011-04
影响因子：
3.7
通讯作者：
G. Lube;H. Huppert;R. Sparks;A. Freundt
中科院分区：
文献类型：
--
作者：
G. Lube;H. Huppert;R. Sparks;A. Freundt
我们目前的实验结果的崩溃的矩形柱砂粗糙，倾斜，平行壁通道。基底倾角θ在4.2°和25°之间变化的结果与以前水平通道的结果进行了比较。浅水理论可以有效地与通过量纲分析获得的比例关系相结合，以产生最大跳动距离、最大存款高度和达到最大跳动的时间的解析函数。虽然该理论很好地预测了存款的最大长度，但它通常高估了终止时间。惯性流的特点是由一个移动的内部界面分离上部流动和下部静态区域的材料。在崩溃的初始自由落体阶段，内部界面下方的沉积面积（=每单位宽度的体积）随时间的平方根而变化，与柱的初始高度和通道倾斜度无关。在随后的横向扩展阶段，沉积速率随着基底倾角的增大或初始高度的减小而减小。在任何固定距离处的局部沉积速率是恒定的，取决于柱的纵横比、通道倾斜度和纵向位置，但不随流速和深度而变化。在横向扩展阶段，流层中的垂向流速剖面具有普遍的形式，与流深和流速无关。它们可以通过作为通道倾斜度的函数的剪切速率和描述参与流动的柱的分数的长度尺度来表征。
We present experimental results for the collapse of rectangular columns of sand down rough, inclined, parallel-walled channels. Results for basal inclination θ varying between 4.2° and 25° are compared with previous results for horizontal channels. Shallow-water theory can be usefully combined with scaling relationships obtained by dimensional analysis to yield analytical functions of the maximum runout distance, the maximum deposit height and the time to reach the maximum runout. While the theory excellently predicts the maximum lengths of the deposit it generally overestimates the runout time. The inertial flows are characterized by a moving internal interface separating upper flowing and lower static regions of material. In an initial free-fall phase of collapse the deposited area (= volume per unit width) below the internal interface varies with the square-root of time, independent of the initial height of the column and channel inclination. In the subsequent, lateral spreading phase the deposition rate decreases with increasing basal inclination or with decreasing initial height. The local deposition rate at any fixed distance is a constant, dependent on the column aspect ratio, the channel inclination and the longitudinal position, but invariant with flow velocity and depth. In the lateral spreading phase, vertical velocity profile in the flowing layer take a universal form and are independent of flow depth and velocity. They can be characterized by a shear rate as a function of channel inclination and a length scale describing the fraction of the column involved in flow.