再论紊流推移质输运中的坡度影响：垂直流结构和输运率定标的结果
Revisiting slope influence in turbulent bedload transport: consequences for vertical flow structure and transport rate scaling
摘要：
在过去的一个世纪里，重力驱动的湍流推移质输运在地球表面过程（如自然河床形态演变）中的重要性得到了广泛的研究。在目前的贡献，纵向通道倾斜角的影响重力驱动的湍流推移质输运的研究在一个理想化的框架，考虑稳定和均匀的流动条件。从基于两相连续方程的解析分析，示出：（i）临界希尔兹数的经典斜率修正是基于浮力的错误公式，（ii）坡度的影响不仅限于临界希尔兹数，而且影响整个输运公式，以及（iii）压力驱动和重力-从坡度影响的观点来看，驱动的湍流推移质输运是不等价的。通过对颗粒流驱动机制的进一步分析，发现纵坡不仅影响床层剪切力和颗粒层阻力，而且影响颗粒层内部的流体流动，从而导致推移质向泥石流的转化。这些耦合机制的相对影响，使我们能够理解的颗粒流的垂直结构的演变，并预测运输速率标度律作为一个重新缩放的希尔兹数的函数。理论分析验证耦合流体离散元模拟的理想化的重力驱动的湍流推移质输运，在很宽的范围内的盾数值，密度比和通道倾角。特别是，所有的数据显示崩溃到一个主曲线时，考虑到泥沙输移率作为一个函数的建议重新缩放的希尔兹数。
英文摘要：
Gravity-driven turbulent bedload transport has been extensively studied over the past century in regard to its importance for Earth surface processes such as natural riverbed morphological evolution. In the present contribution, the influence of the longitudinal channel inclination angle on gravity-driven turbulent bedload transport is studied in an idealised framework considering steady and uniform flow conditions. From an analytical analysis based on the two-phase continuous equations, it is shown that : (i) the classical slope correction of the critical Shields number is based on an erroneous formulation of the buoyancy force, (ii) the influence of the slope is not restricted to the critical Shields number but affects the whole transport formula and (iii) pressure-driven and gravity-driven turbulent bedload transport are not equivalent from the slope influence standpoint. Analysing further the granular flow driving mechanisms, the longitudinal slope is shown to not only influence the fluid bed shear stress and the resistance of the granular bed, but also to affect the fluid flow inside the granular bed - responsible for the transition from bedload transport to debris flow. The relative influence of these coupled mechanisms allows us to understand the evolution of the vertical structure of the granular flow and to predict the transport rate scaling law as a function of a rescaled Shields number. The theoretical analysis is validated with coupled fluid-discrete element simulations of idealised gravity-driven turbulent bedload transport, performed over a wide range of Shields number values, density ratios and channel inclination angles. In particular, all the data are shown to collapse onto a master curve when considering the sediment transport rate as a function of the proposed rescaled Shields number.
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