球层中的非线性自由热对流——变粘度模型.PDFVIP

球层中的非线性自由热对流——变粘度模型 朱涛 冯锐 （中国地震局地球物理研究所，100081，北京） 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。 关键词： 变粘度 自由热对 流非线性 环型场分量 Nonlinear thermal free convection in spherical shell — variable viscosity model Zhu Tao Feng Rui (Institute of Geophysics, China Earthquake Administration, Beijing 100081,China) Abstract: In mantle convection model, the mantle viscosity is generally assumed constant or dependent on depth. In this paper, Laterally variable viscosity is introduced into mantle convection model adding a latitude-dependent viscosity with small fluctuation to constant mantle viscosity. The features of toroidal field dependent on depth and Rayleigh number are discussed under two boundary conditions, in which top boundary is rigid and bottom stress-free (R-F boundary for short) and the other both are rigid (R-R boundary for short). The results show that the energy of toroidal field mainly concentrate in the middle and upper parts of spherical shell and the ratio of its rms velocity value to that of total velocity field is only a few percent and hardly dependent on Rayleigh number which has great effect on the convection pattern of toroidal field. The convection pattern and velocity of toroidal field have obvious difference in latitude, which clearly reflects the effect of lateral mantle viscosity variation on convection pattern. These preliminary results give us a possible ro