Laboratory experiments and simulations for solitary internal waves with trapped cores
Laboratory experiments and simulations for solitary internal waves with trapped cores
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具有困芯的孤立内波的实验室实验和模拟
DOI：
10.1017/jfm.2014.501
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发表时间：
2014
影响因子：
3.7
通讯作者：
K. Helfrich
中科院分区：
文献类型：
--
作者：
P. Luzzatto‐Fegiz;K. Helfrich
摘要我们利用粘性数值模拟的方法，同时测量了具有俘获核的孤立内波中的速度和密度。我们的装置包括一个薄的层状层(大约占总流体深度的15%)，覆盖着一个深而均匀的层。我们考虑波在自由面附近传播，以及在刚性防滑盖子附近传播。在自由面情况下，所有捕获的核心波都表现出很强的剪切不稳定性。我们认为Marangoni效应是造成这种不稳定性的原因，并利用我们的速度测量结果进行了支持这一假设的定量计算。在实验范围内，这些表面张力效应似乎很难避免。相比之下，我们用防滑盖子进行的实验产生了大芯数的强波。为了考虑更大的波幅，我们使用了一个更长的虚拟水箱，用粘性数值模拟来补充我们的实验。在存在重叠的地方，我们的实验和模拟是很一致的。为了给捕获的核心提供一个可靠的定义，我们建议将它定义为拉格朗日相干结构(而不是像传统方法那样使用封闭的流线)。这种结构对速度场中的小误差和小的三维效应不那么敏感。为了只保持平衡附近的流动，我们引入了一个基于岩心密度变化率的稳定性判据。我们利用这个准则在我们的实验和模拟中成功地选择了一类具有良好崩塌特性的准定常鲁棒流。核心环流较小(最多只占斜压波环流的10%左右)。核心密度基本上是均匀的；在核心区域，密度的标准偏差不到整个密度范围的4%。我们还计算了这些波的环流、动能和有效势能。我们发现，这些结果与Dubreil-Jacotin-Long理论对于具有均匀密度无旋核心的波的预测是一致的，除了偏移量，我们认为它与粘性效应有关。最后，通过计算Richardson数场和基于Taylor-Goldstein方程的时间稳定性分析，我们的结果与文献中的经验稳定性准则是一致的。
Abstract We perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15 % of the overall fluid depth) overlaying a deep homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult to avoid at the experimental scale. By contrast, our experiments with a no-slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer virtual tank. Where overlap exists, our experiments and simulations are in good agreement. In order to provide a robust definition of the trapped core, we propose bounding it as a Lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady robust flows that exhibit good collapse in their properties. The core circulation is small (at most, around 10 % of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4 % of the full density range. We also calculate the circulation, kinetic energy and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin–Long theory for waves with a uniform-density irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson-number fields, and performing a temporal stability analysis based on the Taylor–Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature.
影响因子：
3.7
作者：
Fructus, Dorian;Carr, Magda;Davies, Peter A.
通讯作者：
Davies, Peter A.