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<sup>*</sup>

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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^*

基金项目: * 国家自然科学基金

1.
Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, P. R. China;
2.
Department of Environmental Science Research, South China Sea Institute of Oceanology, Academia Sinica, Guangzhou 510301, P. R. China

摘要: 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0s-r_sc<<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。
- 温盐双扩散系统 /
- 周期解 /
- 稳定性
Abstract: A shortout analytic method of stability in Strong non-linear autonomous system is introduced into stability analysis of the themohaline double-diffusive system.Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions.For linear periodic solution in infinitesimeal motion the existence range of monotomic branch and oscillatory branch are outilined.The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value μ_c in this case of 0s-r_sc<<1.The stability conclusions under different direction of vortex are drawn out .
- thermohaline double-diffusive system /
- periodic solution /
- stability

[1]	H.E.Huppert and D.R.Moore,Nonlinear double-diffusive convection,J.Fluid Mech.,78(1976).821-854.
[2]	H.E.Huppert,Transitions in double-diffusive convection,Nature,263(1976),20-22.
[3]	E.Knobloch and M.R.E.Proctor,Nonlinear periodic convection in double-diffusive sy stems.J:Fluid Mech.,108(1981),291-336.
[4]	J.Marotzke and P.Welander.Instability and multiple steady states in a meridional-plan model of the thermohaline circulation,Tellus,40A(1988),149-162.
[5]	N.O.Weiss,Convection in an imposed magnetic field J.Fluid Mech.,108(1981).247-289.
[6]	徐兆、黄祯彪,非线性振子极限环灼实用分析法,力学与实践,11( 1988 ),6-11.
[7]	徐兆、张涤明,温盐双扩散系统非线性周期对流稳定性分析.中山大学学报(自然科学版),28(1989 ),1-4.