Analysis of surface wave formation of icicles and its application to the formation of stalactites

本文提出了一种新的冰柱表面形成模型，并进行了相关的数学工作，同时进行了一些实验和野外工作，发现对于冰柱问题，当考虑水的表面张力时，我们不能表达实验事实（特定波长的表面波的形成）。进一步的考虑是必要的，以找到一些物理因素来解释实验结果。另一方面，上野的类似模型说，每个实验结果都可以解释。然而，首先，他的温度场边界条件在物理上是不能接受的。第二，他提出的波浪向上运动的结果被冰柱内部气泡的痕迹所证实。但是，通过数百次的视频拍摄和冰柱内部晶体形成的图像，我们无法找到冰柱表面波浪的明确运动。因此，我们得出结论，没有理由把波动和冰柱内部气泡的踪迹联系起来。而且应该说这个问题还是一个开放性的问题。我们将进一步继续这方面的研究。接下来我们考虑了相关的数学问题。一个是关于表面张力。我们从统计力学的观点来考虑它的值，然后尝试从悬滴的形式来测量它的问题。进一步从高斯曲率的角度讨论了雪粒的形态。这实际上与表面能有关。另一方面，为了研究热问题与地表形成的关系，本文采用相场模型，并与通常的理论进行比较，在北海道、岩手县和冲绳诸岛的6个洞穴中进行了冰石笋、钟乳石、石笋和缘石的野外观测。这些数据被用来为这些对象构建新的形态学理论。

We have proposed a new model for the surface formation of icicle, we also proposed some mathematically related works, and some experiments and some field works are done.For the problem of icicle, it was found that we cannot express the experimental fact (formation of surface wave with specific wave length) when we take into account the surface tension of water. Further consideration is necessary to find some physical factors which explain the experimental results. On the other hand, the similar model made by Ueno says that every experimental result can be explained. However, first, his boundary condition for the temperature field can not be accepted physically. Second, his result which suggests the motion of wave going upward is asserted to be proved by the trace of bubbles inside of icicles. But we cannot find the explicit motion of waves on the surface of icicle by hundreds video filming and the picture of formation of many crystals inside of icicles. So we have concluded that there is no reason to connect the wave motion and the trace of bubbles inside of icicles. And it should be said that this problem is still an open one. We will further continue the research on this point.Next we have considered the related mathematical problems. One is about the surface tension. We considered its value from the statistical mechanics view point, and next tried the problem of measurement of one from the form of pendant drop. Further the morphology of snow grains from the view point of Gaussian curvature is discussed. This is really related to the surface energy. On the other hand, To study the relation between the thermal problem and surface formation, phase field model is studied to compare to the usual theories.The field works to take the data on ice-stalagmites, stalactites, stalagmites and rim stones are done in 6 caves in Hokkaido, Iwate prefecture and Okinawa islands. These data are used to construct the new morphological theories for these objects.