Dynamics of interfaces and layers in a stratified turbulent fluid
Dynamics of interfaces and layers in a stratified turbulent fluid
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分层湍流流体中界面和层的动力学
DOI：
10.1063/1.1752928
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发表时间：
1997
影响因子：
4.6
通讯作者：
W. Park
中科院分区：
文献类型：
--
作者：
W. Park
本文建立了一个分层湍流混合模型。该模型以水平平均垂直浮力梯度和湍动能密度为变量。启发式的“混合长度”参数导致一组耦合的抛物型微分方程。提出了一种特殊形式的机械强迫;对于某些参数值的浮力通量和浮力梯度之间的关系是非单调的，这导致线性分层的平衡不稳定。不稳定性导致浮力剖面中形成台阶和界面。与以前的模型相比，该模型在数学上是很好的，并且界面的平衡厚度远大于分子扩散的预期厚度。湍流混合过程可以根据初始分层的强度采取三种形式之一。当层化较弱时，不稳定性不存在，混合平稳地使浮力均匀化。在中等强度的分层，层和界面迅速形成在一个实质性的内部区域所界定的边缘层与通量条件的边界。随着界面漂移到一起并合并，内部模式随后发展得更慢;同时，边缘层无情地推进到内部。最终，边缘层在中间相遇，层的内部图案被擦除。任何剩余的结构随后平稳地衰减到均匀状态。弱分层和中间分层的情况都符合实验现象学。该模型预测了第三种情况，具有强分层，尚未发现实验，其中中心区域是线性稳定的，没有步骤形成。然而，边缘层是不稳定的;混合锋形成，然后侵蚀到内部。
This paper formulates a model of mixing in a stratified and turbulent fluid. The model uses the horizontally averaged vertical buoyancy gradient and the density of turbulent kinetic energy as variables. Heuristic ‘mixing-length’ arguments lead to a coupled set of parabolic differential equations. A particular form of mechanical forcing is proposed; for certain parameter values the relationship between the buoyancy flux and the buoyancy gradient is non-monotonic and this leads to an instability of equilibria with linear stratification. The instability results in the formation of steps and interfaces in the buoyancy profile. In contrast to previous ones, the model is mathematically well posed and the interfaces have an equilibrium thickness that is much larger than that expected from molecular diffusion. The turbulent mixing process can take one of three forms depending on the strength of the initial stratification. When the stratification is weak, instability is not present and mixing smoothly homogenizes the buoyancy. At intermediate strengths of stratification, layers and interfaces form rapidly over a substantial interior region bounded by edge layers associated with the fluxless condition of the boundaries. The interior pattern subsequently develops more slowly as interfaces drift together and merge; simultaneously, the edge layers advance inexorably into the interior. Eventually the edge layers meet in the middle and the interior pattern of layers is erased. Any remaining structure subsequently decays smoothly to the homogeneous state. Both the weak and intermediate stratified cases are in agreement with experimental phenomenology. The model predicts a third case, with strong stratification, not yet found experimentally, where the central region is linearly stable and no steps form there. However, the edge layers are unstable; mixing fronts form and then erode into the interior.