Hamiltonian theory for motions of bubbles in an infinite liquid
Hamiltonian theory for motions of bubbles in an infinite liquid
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DOI：
10.1017/s002211208700212x
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发表时间：
1987-08
影响因子：
3.7
通讯作者：
T. Benjamin
中科院分区：
文献类型：
--
作者：
T. Benjamin
一般的动力学问题的气泡在无限广阔的理想液体中移动讨论的立场，哈密顿理论，这是赞赏的基础上连接对称性与守恒定律，并确定变分原理，描述稳定的运动。容差是由表面张力和一个任意的气体法律有关的压力和体积的气泡内容，但特别注意的是，模型的体积是恒定的。在§中，最详细的一部分的文件，一个全面的理论，代表自由表面参数化，因此适用于全球的时间。守恒定律的能量和线性和角度分量的冲动，简单地遵循各自的对称性;伽利略的方差和缩放对称性的后果也进行了探讨。最后，在§中，稳定的平移，自旋和螺旋运动的变分特征进行了解释。在§3中，一个形式上更简单的哈密顿理论被证明是从自由表面可以在正交坐标系中表示的适度限制性假设导出的;并且注意到了与圆柱坐标的使用有关的一些特殊细节。对于沿对称轴沿着稳定平移的气泡，第4.1节给出了瑞利原理支持的近似计算。定常螺旋运动在§5中讨论;基于形状的椭球近似的估计在§5.1中给出;关于稳定性的一些推测在§5.2中讨论。第6节简要介绍了处理多连通泡的一般化方法。
The general dynamical problem for bubbles moving in an infinite expanse of perfect liquid is discussed from the standpoint of Hamiltonian theory, which is appreciated as a basis for linking symmetries with conservation laws and for identifying variational principles that describe steady motions. Allowance is made for surface tension and for an arbitrary gas law relating the pressure and volume of the bubble contents, but particular attention is paid to models where the volume is constant. In §, the most detailed part of the paper, a comprehensive theory is developed which represents the free surface parametrically and so applies globally in time. Conservation laws for energy and for linear and angular components of impulse are shown to follow simply from respective symmetries; consequences of Galilean in variance and of a scaling symmetry are also explored. Finally in §, variational characterizations of steady translational, spinning and spiralling motions are explained. In §3 a formally simpler Hamiltonian theory is shown to derive from the mildly restrictive assumption that the free surface can be represented in an orthogonal coordinate system; and some special details attending the use of cylindrical coordinates are noted. For bubbles steadily translating along an axis of symmetry, approximate calculations supported by Rayleigh's principle are presented in §4.1. Steadily spiralling motions are treated in §5; estimates based on spheroidal approximations to shape are presented in §5.1; and some speculations about stability are discussed in §5.2. A brief account of generalizations dealing with multiply connected bubbles is given in §6.