European Journal of Mechanics - B/Fluids ( IF 2.5 ) Pub Date : 2020-12-26 , DOI: 10.1016/j.euromechflu.2020.12.010 T. Zemach
Consider the propagation of a gravity current (GC) sustained by a source of a fluid of density and constant volume rate into an ambient fluid of height and density over a permeable bed. The porous layer of a given length is located at the bottom of the container. Assume Boussinesq and large Reynolds-number flow. We present a new model for the prediction of the thickness and depth-averaged velocity as functions of distance and time . We show that during the propagation, the GC can develop four main stages: two first stages occur before the dense fluid enters the permeable domain and two follow after that. The second and the fourth stages are steady-states with constant height and velocity; while during the third phase the current is sinking into a substrate: its height is decreasing and its velocity is increasing. We show that the significant parameter of the problem is the length of the gap . We derive a compact implicit expression which connects the heights of the current during the second and the fourth steady-state phases. Comparisons with published experiments show good qualitative agreement, however, quantitative comparison was not possible.
中文翻译:
在恒定的流入重力流在多孔底部上传播时
考虑密度流体源所承受的重力流(GC)的传播 和恒定的体积率 进入高度高的环境流体 和密度 在可渗透的床上 给定长度的多孔层位于容器的底部。假设Boussinesq和雷诺数大。我们提出了一种预测厚度的新模型 和深度平均速度 作为距离的函数 和时间 。我们表明,在传播过程中,GC可以发展为四个主要阶段:两个第一阶段发生在致密流体进入渗透性区域之前,第二阶段随后发生。第二和第四阶段是高度和速度恒定的稳态。而在第三阶段,电流正在沉入基板中:其高度在减小,速度在增加。我们表明问题的重要参数是间隙的长度。我们导出一个紧凑的隐式表达式,该表达式将第二和第四稳态阶段的电流高度连接起来。与已发表实验的比较显示出良好的定性一致性,但是,无法进行定量比较。