球层中的非线性自由热对流——变粘度模型  

NONLINEAR FREE THERMAL CONVECTION IN A SPHERICAL SHELL: A VARIABLE VISCOSITY MODEL

作　　者：朱涛[1,2] 冯锐[3] 

机构地区：[1]中国地震局兰州地震研究所 [2]中国北京100081中国地震局地球物理研究所 [3]中国地震局地球物理研究所

出　　处：《地震学报》2005年第2期194-204,共11页Acta Seismologica Sinica

基　　金：国家自然科学基金重点项目(49834020)资助.

摘　　要：粘度为常数或仅随深度变化是地幔对流模型中常用的假设. 本文在常粘度背景下, 通过假定小扰动粘度在纬向上的变化形式, 将粘度的横向变化引入地幔对流模型中, 并给出了变粘度地幔对流模型的数值解法. 对外边界为刚性、内边界为应力自由(简记为R F边界)和内外边界均为刚性(简记为R R边界)边界的两种模型进行了计算, 对比了不同模型、深度和瑞利数时的环型场的变化特征. 注意到环型场能量主要集中在球层的中、上部区域, 其速度仅占总速度的几个百分点, 这个比例几乎不随瑞利数的变化而改变, 但其对流图样受瑞利数的影响较大. 环型场的对流形态和速度的分布特征表现出了明显的纬向差异, 这一结果清晰地反映出地幔粘度的横向变化对对流形态的影响. 目前的工作还只是初步的, 但为我们探讨全球大地构造上的某些现象, 例如南北半球的不对称性和差速旋转问题提供了一种可能的研究思路.In mantle convection models, the mantle viscosity is generally assumed constant or dependent on depth. In this paper, a laterally variable viscosity is introduced into mantle convection model in which the mantle viscosity consists of a constant background and latitude dependent viscosity with small fluctuations. The features of toroidal field dependent on depth and Rayleigh number are discussed under two boundary conditions, the top rigid and bottom stress free boundaries (R F boundary for short) and both rigid ones (R R boundary for short), respectively. The results show that the energy of toroidal field mainly concentrates in the middle and upper parts of a spherical shell, and the ratio of toroidal to total velocities amounts to only a few percents and hardly depends on Rayleigh number, while the convection patterns of toroidal field have been strongly affected by Rayleigh number. It is found that the convection patterns and velocities of toroidal field have obvious differences in latitudinal direction, which clearly reflects the effects of lateral mantle viscosity variations on the convection patterns. These preliminary results give us a possible hint to study some global tectonic phenomena, e.g. the asymmetry of the southern and northern hemispheres and the earth′s differential rotation.

关 键 词：变粘度 自由热对流 环型场分量 

分 类 号：P314.2[天文地球—固体地球物理学] P541[天文地球—地球物理学]