Laney D, Bremer P T, Mascarenhas A, Miller P, Pascucci V
Lawrence Livermore National Laboratory, USA.
IEEE Trans Vis Comput Graph. 2006 Sep-Oct;12(5):1053-60. doi: 10.1109/TVCG.2006.186.
When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes known as Rayleigh-Taylor instability. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion. We present a new approach to analyze Rayleigh-Taylor instabilities in which we extract a hierarchical segmentation of the mixing envelope surface to identify bubbles and analyze analogous segmentations of fields on the original interface plane. We compute meaningful statistical information that reveals the evolution of topological features and corroborates the observations made by scientists. We also use geometric tracking to follow the evolution of single bubbles and highlight merge/split events leading to the formation of the large and complex structures characteristic of the later stages. In particular we (i) Provide a formal definition of a bubble; (ii) Segment the envelope surface to identify bubbles; (iii) Provide a multi-scale analysis technique to produce statistical measures of bubble growth; (iv) Correlate bubble measurements with analysis of fields on the interface plane; (v) Track the evolution of individual bubbles over time. Our approach is based on the rigorous mathematical foundations of Morse theory and can be applied to a more general class of applications.
当重流体置于轻流体之上时，界面处微小的垂直扰动会产生一种由上升气泡和下降尖峰组成的特征结构，即瑞利 - 泰勒不稳定性。在过去的半个世纪里，瑞利 - 泰勒不稳定性受到了广泛关注，因为它对于理解许多自然和人造现象至关重要，从超新星中重元素的形成速率到惯性约束聚变胶囊的设计。我们提出了一种分析瑞利 - 泰勒不稳定性的新方法，即提取混合包络面的分层分割以识别气泡，并分析原始界面平面上场的类似分割。我们计算有意义的统计信息，以揭示拓扑特征的演变，并证实科学家们的观察结果。我们还使用几何跟踪来追踪单个气泡的演变，并突出导致后期阶段特征性的大型复杂结构形成的合并/分裂事件。特别是，我们（i）给出气泡的形式化定义；（ii）分割包络面以识别气泡；（iii）提供一种多尺度分析技术来生成气泡生长的统计量度；（iv）将气泡测量与界面平面上场的分析相关联；（v）随时间追踪单个气泡的演变。我们的方法基于莫尔斯理论的严格数学基础，可应用于更广泛的一类应用。
