等深度竖直圆柱中两层流体的晃荡
Sloshing of a two-layer fluid in a vertical cylinder of constant depth
AI总结：
该研究针对等深度有限深竖直圆柱内两层流体的晃荡问题，推导了用横截面Neumann拉普拉斯本征值显式表示的两类本征频率，分析了其相关性质并通过数值算例验证。
摘要：
本文研究了填充有两层流体的等深度有限深竖直圆柱的晃荡本征值与本征函数。研究得到了两类本征频率，其表达式可通过圆柱横截面这一二维区域上的Neumann拉普拉斯算子的本征值显式表示。其中一类本征频率的特性与均质流体晃荡的本征频率相似，另一类则在密度比接近1时包含大量足够小的频率。针对任意横截面的圆柱，本文探究了本征频率的多种性质，包括其随界面深度、密度比的变化关系，以及本征值计数函数的渐近行为。通过无径向挡板和带径向挡板的圆柱的数值算例，阐释了本征值及对应本征模的特性。
英文摘要：
Sloshing eigenvalues and eigenfunctions are studied for vertical cylinders of constant, finite depth occupied by a two-layer fluid. Two families of eigenfrequencies are obtained in the form expressing them explicitly via the eigenvalues of the Neumann Laplacian in the two-dimensional domain\, -- \,cylinder's cross-section. Eigenfrequencies belonging to one of the families behave similar to those that describe sloshing in a homogeneous fluid, whereas the other family includes a large number of sufficiently small frequencies provided the ratio of densities is close to unity. Various properties of eigenfrequencies are investigated for cylinders of arbitrary cross-section; they include the dependence on the interface depth and the ratio of densities, the asymptotics of the eigenvalue counting function. The behaviour of eigenvalues and the corresponding eigenmodes is illustrated by numerical examples for circular cylinders without and with a radial baffle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
