Slow spreading of a sheet of Bingham fluid on an inclined plane
Slow spreading of a sheet of Bingham fluid on an inclined plane
复制标题
宾汉流体片在斜面上的缓慢扩散
DOI：
10.1017/s0022112089002685
复制
发表时间：
1989
影响因子：
3.7
通讯作者：
C. Mei
中科院分区：
文献类型：
--
作者：
Kofei Liu;C. Mei
为了研究含高粘性粘土颗粒的流体泥浆的动力学特性，提出了一个宾汉塑性流体薄层在斜面上缓慢流动的理论。在润滑理论的近似基础上讨论了其物理性质。由于屈服应力的存在，当宾汉流体处于静态平衡时，自由表面不一定水平，当流体处于稳定流动时，自由表面也不一定平行于平床。然后，我们表明，有各种重力流，可以在一个恒定的速度和相同的配置文件。一种类型的实验确认。通过求解非线性偏微分方程，研究了上游稳定泄流或有限流体质量突然释放到另一流体层上所引起的瞬变流动。在第一种情况下，有一个泥锋，它最终作为一个稳定的重力流以恒定的速度传播。在第二种情况下，当环境层足够浅，没有初始运动时，由新流体引起的流动可以在扰动行进有限距离后终止。最后的蔓延的程度进行检查。扰动由于外部压力平行于自由表面的旅行也检查。特别是发现，压力梯度的行进局部脉冲不仅产生与强制压力一起沿着行进的局部泥浆扰动，而且进一步留下永久足迹。
To study the dynamics of fluid mud with a high concentration of cohesive clay particles, we present a theory for a thin sheet of Bingham-plastic fluid flowing slowly on an inclined plane. The physics is discussed on the approximate basis of the lubrication theory. Because of the yield stress, the free surface need not be horizontal when the Bingham fluid is in static equilibrium, nor parallel to the plane bed when in steady flow. We then show that there is a variety of gravity currents that can advance at a constant speed and with the same profile. Experimental confirmation of one type is presented. By solving a nonlinear partial differential equation, transient flows due either to a steady upstream discharge or to the sudden release of a finite fluid mass on another fluid layer are studied. In the first case there is a mud front which ultimately propagates as a constant speed as a steady gravity current. In the second case, when the ambient layer is sufficiently shallow that there is no initial motion, the flow induced by the new fluid can terminate after the disturbance has travelled a finite distance. The extent of the final spread is examined. Disturbances due to an external pressure travelling parallel to the free surface are also examined. It is found in particular that a travelling localized pulse of pressure gradient not only generates a localized mud disturbance which travels along with the forcing pressure, but further leaves behind a permanent footprint.