Bounded dam-break flows with tailwaters
Bounded dam-break flows with tailwaters
复制标题
含尾水的有界溃坝流
作者：
Alex Goater;A. Hogg
摘要利用非线性浅水方程组研究了重力驱动下的水库溃坝，溃坝后的尾水是一个初始静止的流体层。运动是解决使用速端变换的控制方程，允许的速度和深度的浅流层的解决方案，通过分析技术来构建。流动的前部以孔的形式出现，流体的深度通过该孔不连续地跳跃到尾水深度。锋面的速度最初是恒定的，但一旦水库的有限范围开始影响运动，就会逐渐减慢。然后，根据尾水相对于水库初始深度的深度，出现各种现象。如果尾水足够深，则在水库后壁附近出现一个静止流体区域，随后是一个速度为负的区域。它还表明，对于非零尾水深度，连续的解决方案的速度和高度的流动层故障后，一个足够的时间，并开发一个内部孔，位置和时间的起始直接计算从准解析解。
Abstract The gravitationally driven collapse of a reservoir into an initially stationary layer of fluid, termed the tailwater, is studied using the nonlinear shallow water equations. The motion is tackled using the hodograph transformation of the governing equation which allows the solutions for velocity and depth of the shallow flowing layer to be constructed by analytical techniques. The front of the flow emerges as a bore across which the depth of the fluid jumps discontinuously to the tailwater depth. The speed of the front is initially constant, but progressively slows once the finite extent of the reservoir begins to influence the motion. There then emerges a variety of phenomena depending upon the depth of the tailwater relative to the initial depth of the reservoir. Provided that the tailwater is sufficiently deep, a region of quiescent fluid emerges adjacent to the rear wall of the reservoir, followed by a region within which the velocity is negative. Also it is shown that for non-vanishing tailwater depths, continuous solutions for the velocity and height of the flowing layer breakdown after a sufficient period and develop an interior bore, the location and time of inception of which are calculated directly from quasi-analytical solutions.