可压缩流体的Rayleigh-Taylor和Kelvin-Helmholtz不稳定性

在状态方程为压力是密度的任意单值函数形式情况下，运用小扰动分析和奇异摄动法，给出了流体微扰方程渐近解和界面不稳定性的色散关系. 分析表明：对Rayleigh-Taylor不稳定性，在重力场作用下流体可压缩性形成的密度分布是致稳因素；而扰动流体的膨胀收缩效应助长不稳定性的发展；上层重流体的可压缩性是稳定因素，下层轻流体可压缩性是失稳因素. 而对Kelvin-Helmholtz不稳定性，流体可压缩性助长扰动的发展，是不稳定因素.

Rayleigh-taylor and kelvin-helmholtz instability of compressible fluid

The role of fluid compressibility in Rayleigh-Taylor and Kelvin-Helmholtz instability is studied when the state equation of compressible fluid is an arbitrary function of density and pressure. It shows that in the Rayleigh-Taylor instability the density distributing induced by the gravity is a stable factor, while the fluid expanding and compressing effect is an instable factor. It also shows that in the Rayleigh-Taylor instability the compressibility of upper heavier fluid is a stable factor, while the compressibility of lower lighter fluid is an instable factor, and in the Kelvin-Helmholtz instability the compressibility of upper and lower fluid is an instable factor.