Consider the propagation of a gravity current (GC) sustained by a source of a fluid of density ${\rho }_c$ and constant volume rate $Q$ into an ambient fluid of height $H$ and density ${\rho }_a$ over a permeable bed. The porous layer of a given length $\Delta x_p$ 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 $h$ and depth-averaged velocity $u$ as functions of distance $x$ and time $t$. 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 $\Delta x_p$. 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.

考虑密度流体源所承受的重力流（GC）的传播 ${\rho }_C$ 和恒定的体积率 $问$ 进入高度高的环境流体 $H$ 和密度 ${\rho }_{\mathrm{一种}}$在可渗透的床上 给定长度的多孔层$\Delta X_p$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$H$ 和深度平均速度 $ü$ 作为距离的函数 $X$ 和时间 $Ť$。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$\Delta X_p$。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。