The propagation of a gravity current into a linearly stratified fluid
The propagation of a gravity current into a linearly stratified fluid
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DOI：
10.1017/s0022112001007054
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发表时间：
2002-02
影响因子：
3.7
通讯作者：
T. Maxworthy;J. Leilich;J. Simpson;E. Meiburg
中科院分区：
文献类型：
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作者：
T. Maxworthy;J. Leilich;J. Simpson;E. Meiburg
重重力流的恒定初始传播速度 (V) 密度为 ρC，从船闸后面释放并沿着含有线性分层流体的储罐底部边界，已通过实验测量并进行了数值计算。分层的从下到上的密度差为 (ρb−ρ0)，其固有频率为 N。对于给定的释放流体深度 (h) 与总深度 (H) 的比率，我们发现无量纲内部弗劳德数 Fr = V/NH 与锁的长度无关，并且是参数 R = (ρC−ρ0)/(ρb−ρ0) 的对数函数，除非 h/H 和 R 值接近团结。该参数 R 是水流 (ρC−ρ0) 和分层 (ρb−ρ0) 相对强度的一种可能度量。对于所有测试的状态，在该恒定速度状态结束之前电流传播的距离 (Xtr)（以 h 为比例）被发现是 Fr 的唯一函数。在该运动阶段之后，对于 Fr 的亚临界值，即小于 1/π，内波与电流的相互作用导致其前缘速度振荡。对于超临界值，速度衰减对于测试的几何形状是单调的。已发现包含无滑移底部边界条件的二维数值模型与实验速度大小在 ±1:5% 范围内一致。
The constant initial speed of propagation (V) of heavy gravity currents, of density ρC, released from behind a lock and along the bottom boundary of a tank containing a linearly stratified fluid has been measured experimentally and calculated numerically. The density difference, bottom to top, of the stratification is (ρb−ρ0) and its intrinsic frequency is N. For a given ratio of the depth of released fluid (h) to total depth (H) it has been found that the dimensionless internal Froude number, Fr = V/NH, is independent of the length of the lock and is a logarithmic function of a parameter R = (ρC−ρ0)/(ρb−ρ0), except at small values of h/H and R close to unity. This parameter, R, is one possible measure of the relative strength of the current (ρC−ρ0) and stratification (ρb−ρ0). The distance propagated by the current before this constant velocity regime ended (Xtr), scaled by h, has been found to be a unique function of Fr for all states tested. After this phase of the motion, for subcritical values of Fr, i.e. less than 1/π, internal wave interactions with the current resulted in an oscillation of the velocity of its leading edge. For supercritical values, velocity decay was monotonic for the geometries tested. A two-dimensional numerical model incorporating a no-slip bottom boundary condition has been found to agree with the experimental velocity magnitudes to within ±1:5%.