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首页> 外文期刊>International journal of non-linear mechanics >Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field
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Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

机译：在任意非均匀重力场中一对任意分层的可压缩流体的稳定性和不稳定性条件

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摘要

The work continues and develops authors' previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a "canonical" form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers). (C) 2017 Elsevier Ltd. All rights reserved.
机译：这项工作在继续进行，并发展了作者先前对均匀重力场中两层非均质可压缩流体系统的稳定性的研究。在这里，我们提出了在任意不均匀的潜在重力场情况下类似问题的解决方案。流体的密度和弹性性质的均衡分层被认为是任意的，并且流体填充的顶部储层上的开口的形状被认为是任意的。平衡的稳定性问题作为非线性弹性体的相应问题，基于静能量准则针对边界所有部分的边界条件进行分析。分析的关键要素是将系统总势能的第二次变化的二次函数转换为“正则”形式，从而确定其符号。利用这种规范形式，我们获得了几乎彼此一致的必要和充分的稳定性条件（这些条件也适用于任意数量的层）。 （C）2017 Elsevier Ltd.保留所有权利。

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