明显障碍物上方两层分层流界面处的非线性动力学
Nonlinear dynamics at the interface of two-layer stratified flows over pronounced obstacles
摘要：
本文模拟海洋问题中的有关情况，在简化的二维情况下，对两层分层流体越过陡峭地形障碍物的流动进行了数值和实验研究。实验结果和数值模拟在低弗劳德数在两层分层流和两个突然的障碍物，半圆柱形和棱柱。我们发现四种不同的制度的流动立即过去的障碍：亚临界（I），内部水跃（II），开尔文-亥姆霍兹在接口（III）和脱落的波涛（IV）。利用水力学理论，得到了确定试验边界的临界条件。此外，临界弗劳德数的依赖关系的障碍物的几何形状进行了调查。从制度III到制度IV的过渡解释与理论稳定性分析。稳定性分析的结果与DPIV测量结果一致。在（IV）区，当上游速度足够大时，我们发现射流的Kelvin-Helmhotz不稳定性产生了波涛的脱落。重要的区别与流动，如冯卡门的街道进行了解释。实验结果和数值模拟之间的显着协议。
英文摘要：
The flow of a two--layer stratified fluid over an abrupt topographic obstacle, simulating relevant situations in oceanographic problems, is investigated numerically and experimentally in a simplified two--dimensional situation. Experimental results and numerical simulations are presented at low Froude numbers in a two-layer stratified flow and for two abrupt obstacles, semi--cylindrical and prismatic. We find four different regimes of the flow immediately past the obstacles: sub-critical (I), internal hydraulic jump (II), Kelvin-Helmholtz at the interface (III) and shedding of billows (IV). The critical condition for delimiting the experiments is obtained using the hydraulic theory. Moreover, the dependence of the critical Froude number on the geometry of the obstacle are investigated. The transition from regime III to regime IV is explained with a theoretical stability analysis. The results from the stability analysis are confirmed with the DPIV measurements. In regime (IV), when the velocity upstream is large enough, we find that Kelvin-Helmhotz instability of the jet produces shedding of billows. Important differences with flows like Von Karman's street are explained. Remarkable agreement between the experimental results and numerical simulations are obtained.
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