Turbulent mixing in stratified fluids: layer formation and energetics
Turbulent mixing in stratified fluids: layer formation and energetics
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分层流体中的湍流混合：层形成和能量学
DOI：
10.1017/s0022112094003915
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发表时间：
1994
影响因子：
3.7
通讯作者：
Anand Gnanadeskian
中科院分区：
文献类型：
--
作者：
Young‐Gyu Park;J. Whitehead;Anand Gnanadeskian
初始盐层结恒定的水与水平移动的垂直杆混合。当混合较弱时，初始的线性密度分布转变为一系列阶跃，这与Phillips(1972)和Posentier(1977)的不稳定性理论相一致。对于更强的混合，没有形成台阶。然而，在所有情况下，由于水平边界处的无通量条件，混合层在顶部和底部边界附近形成，并扩展到内部。划分有步骤和无步骤实验的临界理查森数Re随着雷诺数Re的增加而增加，即RIE≈exp(Re/90 0)。步数随着时间的推移而演变，小的步子先形成，大的步子后来出现。内部似乎达到了一种平衡状态，有一系列静止的台阶。边界混合层继续向内部渗透。他们最终形成了两个相隔一步的混合层，并最终获得了相同的密度，因此流体变得均匀。平衡步骤的长度尺度ls是U/Ni的线性函数，其中U是搅拌棒的速度，Ni是初始分层的浮力频率。混合效率Rf也随密度结构的演化而变化。在这些步骤的开始过程中，Rf显示出两种完全不同的演化模式，这取决于初始状态RIO的整体理查森数。对于里约热内卢，RF最初有所增加。然而，里约热内卢附近的RF下降了。然后，这些步骤达到平衡状态，其中Rf在取决于初始分层的值是恒定的。在平衡状态下，无论内部密度梯度如何，层状结构内部的密度通量都是均匀的。因此，密度(盐分)从底部边界混合层通过分层内部输送到顶部边界混合层，而不改变内部的密度结构。对于RIL>；1，找到了RIL和Rf之间的关系，其中RIL是基于混合层之间界面厚度的Richardson数。随着RIL的增加，Rf减小，这与Phillips/Posentier不稳定性理论中最关键的假设一致。
Water with constant initial salt stratification was mixed with a horizontally moving vertical rod. The initially linear density profile turned into a series of steps when mixing was weak, in agreement with instability theory by Phillips (1972) and Posmentier (1977). For stronger mixing no steps formed. However, in all cases mixed layers formed next to the top and bottom boundaries and expanded into the interior due to the no-flux condition at the horizontal boundaries. The critical Richardson number Rie, dividing experiments with steps and ones without, increases with Reynolds number Re as Rie ≈ exp(Re/900). Steps evolved over time, with small ones forming first and larger ones appearing later. The interior seemed to reach an equilibrium state with a collection of stationary steps. The boundary mixed layers continued to penetrate into the interior. They finally formed two mixed layers separated by a step, and ultimately acquired the same densities so the fluid became homogeneous. The length scale of the equilibrium steps, ls, is a linear function of U/Ni, where U is the speed of the stirring rod and Ni is the buoyancy frequency of the initial stratification. The mixing efficiency Rf also evolved in relation to the evolution of the density structure. During the initiation of the steps, Rf showed two completely different modes of evolution depending on the overall Richardson number of the initial state, Rio. For Rio [Gt ] Rie, Rf increased initially. However for Rio near Rie, Rf decreased. Then the steps reached an equilibrium state where Rf was constant at a value that depended on the initial stratification. The density flux was measured to be uniform in the layered interior irrespective of the interior density gradient during the equilibrium state. Thus, the density (salt) was transported from the bottom boundary mixed layer through the layered interior to the top boundary mixed layer without changing the interior density structure. The relationship between Ril and Rf was found for Ril > 1, where Ril is the Richardson number based on the thickness of the interface between the mixed layers. Rf decreases as Ril increases, consistent with the most crucial assumption of the instability theory of Phillips/Posmentier.