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中文摘要：
本文将Layzer气泡模型推广到任意界面Atwood数情形,得到了自洽的微分方程组.该模型描述了气泡从早期的指数增长阶段到气泡以渐近速度上升的非线性阶段的发展过程,给出了Rayleigh-Taylor（RT）和Richtmyer-Meshkov（RM）不稳定性的二维和三维气泡速度渐近解,还求出了二维和三维RT不稳定性气泡顶点附近速度的解析解.
英文摘要：
We generalize the Layzer＇s bubble model to the cases of two-dimensional and three-dimensional analytical models of an arbitrary interface Atwood number and obtain self-consistent equations.The generalized model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime.The asymptotic bubble velocities are obtained for the Rayleigh-Taylor（RT） and Richtmyer-Meshkov（RM） instabilities.We also report on the two-dimensional and the three-dimensional analytical expressions for the evolution of the RT bubble velocity.
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