The front condition for gravity currents
The front condition for gravity currents
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重力流前沿条件
DOI：
10.1017/s0022112005004933
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发表时间：
2005
影响因子：
3.7
通讯作者：
P. Linden
中科院分区：
文献类型：
--
作者：
B. M. Marino;L. P. Thomas;P. Linden
重力流惯性阶段的自相似平面解与初始参数和由前缘边界条件确定的系数有关。不同的关系已经提出了边界条件的弗劳德数在前面，没有一个有一个健全的理论或实验基础。本文重点考虑适当的弗劳德数的基础上锁交换实验中，扩展的惯性重力流中产生的矩形截面通道的结果。我们使用“顶帽”垂直密度剖面的电流，以获得一个“等效”的深度，定义的剖面具有相同的浮力在每个位置的真实的配置文件。在以前的工作中，我们的实验结果表明，在初始恒速阶段的弗劳德数可以定义在锁定深度。然而，当电流进入相似性阶段时，初始释放条件不再相关，我们发现，弗劳德数更合适地定义在头部的最大高度方面。严格地说，浅水方程的自相似解需要一个使用头部后部高度的前部条件。我们发现，这个后弗劳德数是不恒定的，是一个功能的头部雷诺数的范围400-4500。
Self-similar plane solutions for the inertial stage of gravity currents are related to the initial parameters and a coefficient that is determined by the boundary condition at the front. Different relations have been proposed for the boundary condition in terms of a Froude number at the front, none of which have a sound theoretical or experimental basis. This paper focuses on considerations of the appropriate Froude number based on results of lock-exchange experiments in which extended inertial gravity currents are generated in a rectangular cross-section channel. We use ‘top-hat’ vertical density profiles of the currents to obtain an ‘equivalent’ depth, defined by profiles having the same buoyancy at every position as the real profiles. As in previous work, our experimental results show that in the initial constant-velocity phase the Froude number can be defined in terms of the lock depth. However, as the current enters the similarity phase when the initial release conditions are no longer relevant, we find that the Froude number is more appropriately defined in terms of the maximum height of the head. Strictly speaking, the self-similar solution to the shallow-water equations requires a front condition that uses the height at the rear of the head. We find that this rear Froude number is not constant and is a function of the head Reynolds number over the range 400–4500.