温盐双扩散系统对流扩散周期解的线性与非线性稳定性分析

Stability Analysis of Linear and Nonlinear Periodic Convection in Thermohaline Double-Diffusive Systems

本文对温盐双扩散系统的稳定性问题引入了一种简洁的强非线性自治系统稳定性的分析方法，用摄动理论得到了无穷小运动下线性周期解的单调与振荡分支的存在范围及有限振幅运动下非线性周期解的振荡分支在０＜ｒｓ－ｒｓｃ＜＜１条件下的存在区域及稳定性区域，给出了不同涡旋方向下的稳定性结论．

A shortcut analystic method of stability in strong non-linear autopomous system is introduced into stability analysis of the thermohaline double-diffusive systern.Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions.For linear periodic solution in infinitesimal motion,the existencc range of monotonic branch and oscillatory branch are outlined.The oscillatory branch of nonlinear periodic solution in finite-ampli tude motion has unstable periodic solution when μ is smaller than critical value μc in this case of 0<rs-r3c<<1 The stability conclusions under different direction of vortex are drawn out.