We investigate by theoretical means the motion of a gravity current (GC) released from a lock into an ambient fluid in a horizontal channel of non-rectangular cross-section area (CSA) like triangle, trapezoid or semicircle. The lock contains an internal stratification, in particular a layer of density ${\rho }_L$ overlain by a layer of density ${\rho }_U$, where ${\rho }_o<{\rho }_U<{\rho }_L$ and ${\rho }_o$ is the density of the ambient fluid. Assuming a Boussinesq and large Reynolds flow, we develop a new self-contained model for the prediction of the motion of the GC, in particular the position and speed of the nose $x_N\left(t\right)$ and $u_N\left(t\right)$, where $t$ is the time from release. Upon an appropriate scaling the system of equations and boundary conditions is reduced to a form amenable to analysis and solution by the methods employed for the non-stratified flow. The solution reveals an initial slumping with constant $u_N$, and eventually the transition at $x_V$ to the viscous regime. A self similar phase of the form $x_N\sim t^{\beta }$ can develop only for CSA of power-law shape, in which case the constant $\beta$ depends on the shape but not on the stratification. The stability is also considered, and we show that the flow is stable with few exception. Unfortunately, experimental data for comparisons are not available, and we hope that the sharp present results will motivate the performance of needed experimental tests.

我们通过理论方法研究了从锁释放到非矩形横截面区域（CSA）的水平通道（如三角形，梯形或半圆形）的环境流体中的重力流（GC）的运动。锁具内部分层，特别是一层密度${\rho }_{\mathrm{大号}}$ 覆盖一层密度 ${\rho }_{ü}$， 在哪里 ${\rho }_{Ø}<{\rho }_{ü}<{\rho }_{\mathrm{大号}}$ 和 ${\rho }_{Ø}$是环境流体的密度。假设存在Boussinesq和大雷诺流量，我们开发了一个新的独立模型来预测GC的运动，特别是鼻子的位置和速度$X_{ñ}（Ť）$ 和 ${ü}_{ñ}（Ť）$， 在哪里 $Ť$是从发布开始的时间。在适当地缩放之后，方程式和边界条件的系统将减少为适合于非分层流的方法进行分析和求解的形式。该解决方案显示出恒定的初始坍塌${ü}_{ñ}$，最终过渡到 $X_{\mathrm{伏特}}$粘性的政权。表格的自相似阶段$X_{ñ}〜{Ť}^{\beta }$ 只能针对幂律形状的CSA开发，在这种情况下常数 $\beta$取决于形状而不取决于分层。还考虑了稳定性，并且我们证明了流量稳定，几乎没有例外。不幸的是，尚无用于比较的实验数据，我们希望目前的结果能激发所需实验测试的性能。