On the scaling of stress-driven entrainment experiments
On the scaling of stress-driven entrainment experiments
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关于压力驱动夹带实验的扩展
DOI：
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发表时间：
1979
影响因子：
3.7
通讯作者：
J. Price
中科院分区：
文献类型：
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作者：
J. Price
对Kato & Phillips（1969）和Kantha， Phillips & Azad（1977）的夹带实验（以下简称KP和KPA）进行了分析，以证明夹带观测的更一般和有效的标度。首选标度为[V^{-1} dh/dt = E(R_v)]，其中h为混合层深度，V为混合层平均速度，Rv = B/V2， B为混合层总浮力。在不同的h/L下（L为罐宽），以及内部密度分层（KP）或均匀（KPA）的情况下，这种缩放有效地分解了夹带数据。利用平均动量和浮力守恒方程，从KP和KPA观测值计算出夹带定律E（Rv）。动量守恒方程中包含了一个侧壁阻力项。在0·5 < Rv < 1·0范围内，几乎囊括了所有的KP、KPA数据，E≃5 × 10−4 R−4v。这与表面半射流（Ellison & Turner 1959）和风驱动的海洋表面混合层（Price, Mooers & Van Leer 1978）遵循的夹带定律非常相似。分析表明，当载荷稳定时，Rv为准稳态；当侧壁阻力不大时，在RT = B/U2* （U*为施加应力的摩擦速度）较大范围内，Rv≈0·6。在没有侧壁阻力（h/L消失）的情况下，动量守恒导致U−1*dh/dt = n（0.6）½R−½T，如果内部是线性分层或均匀的，则n = 1 / 2或1。KP、KPA数据显示，在17 < RT < 160的范围内，侧壁阻力的影响可以忽略不计，或者可以通过线性外推法消除。这一结果，连同观察到的侧壁效应的形式和大小，表明平均动量守恒是KP、KPA实验中夹带速率的关键约束。
The entrainment experiments of Kato & Phillips (1969) and Kantha, Phillips & Azad (1977) (hereafter KP and KPA) are analysed to demonstrate a more general and effective scaling of the entrainment observations. The preferred scaling is [ V^{-1} dh/dt = E(R_v), ] where h is the mixed-layer depth, V is the mean velocity of the mixed layer, Rv = B/V2 and B is the total mixed-layer buoyancy. This scaling effectively collapses entrainment data taken at various h/L, where L is the tank width, and in cases in which the interior is density stratified (KP) or homogeneous (KPA). The entrainment law E(Rv) is computed from the KP and KPA observations using the conservation equations for mean momentum and buoyancy. A side-wall drag term is included in the momentum conservation equation. In the range 0·5 < Rv < 1·0, which includes nearly all of the KP, KPA data, E ≃ 5 × 10−4 R−4v. This is very similar to the entrainment law followed by a surface half-jet (Ellison & Turner 1959) and by the wind-driven ocean surface mixed layer (Price, Mooers & Van Leer 1978). The analysis shows that, when forcing is steady, Rv is quasi-steady and, provided that side-wall drag is not large, Rv ≃ 0·6 over a wide range of RT = B/U2*, where U* is the friction velocity of the imposed stress. In the absence of side-wall drag (vanishing h/L) the conservation of momentum then leads to U−1*dh/dt = n(0·6)½ R−½T, where n = ½ or 1 if the interior is linearly stratified or homogeneous. The KP, KPA data show this dependence throughout the range 17 < RT < 160 where the effect of side-wall drag is negligible or can be removed by a linear extrapolation. This result, together with the form and magnitude of the observed side-wall effect, suggests that mean momentum conservation is a key constraint upon the entrainment rate in the KP, KPA experiments.