TURBULENT ENTRAINMENT IN STRATIFIED FLOWS
TURBULENT ENTRAINMENT IN STRATIFIED FLOWS
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DOI：
10.1017/s0022112059000738
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发表时间：
1959-01-01
影响因子：
3.7
通讯作者：
TURNER, JS
中科院分区：
文献类型：
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作者：
ELLISON, TH;TURNER, JS
当倾斜屋顶下的源(或倾斜地板上的源)排放出比其周围更轻的流体时，它可能会作为相对较薄的湍流层流动。这一层的运动受其夹带环境流体的速率控制。提出了一种理论，其中假设夹带量与层的速度与层的总Richardson数的经验函数E(Ri)成正比，该经验函数由Ri=g(ρa-ρ)h/ρAv2定义。这一理论预测，在大多数实际情况下，地层将迅速达到平衡状态，此时Ri不随下游距离变化，而施加在地层上的引力正好被地面或屋顶上的卷吸和摩擦所产生的阻力平衡。在第一种方法中，测量了比它所流过的液体更轻的表面喷流的扩散；在第二种方法中，研究了重液体沿倾斜的通道底部的流动。这些实验表明，随着Ri的增加，E迅速下降，当Ri大于约0.8时，E可能可以忽略不计。理论和实验结果表明，一旦密度差的供应速度已知，就可以对流速进行预测。文中还给出了环境流体为使层运动反转而必须具有的均匀速度的估计值。
When a fluid which is lighter than its surroundings is emitted by a source under a sloping roof (or a heavier fluid from a source on a sloping floor), it may flow as a relatively thin turbulent layer. The motion of this layer is governed by the rate at which it entrains the ambient fluid. A theory is presented in which it is assumed that the entrainment is proportional to the velocity of the layer multiplied by an empirical function, E(Ri), of the overall Richardson number for the layer defined by Ri = g(ρa - ρ) h/ρaV2. This theory predicts that in most practical cases the layer will rapidly attain an equilibrium state in which Ri does not vary with distance downstream, and the gravitational force on the layer is just balanced by the drag due to entrainment together with friction on the floor or roof.Two series of laboratory experiments are described from which E(Ri) can be determined. In the first, the spread of a surface jet of fluid lighter than that over which it is flowing is measured; in the second, a study is made of the flow of a heavy liquid down the sloping floor of a channel. These experiments show that E falls off rapidly as Ri increases and is probably negligible when Ri is more than about 0·8.The theoretical and experimental results allow predictions to be made of flow velocities once the rate of supply of density difference is known. An estimate is also given of the uniform velocity which the ambient fluid must possess in order to cause the motion of the layer to be reversed.