地幔对流与岩石层板块的相互耦合及影响──（Ⅰ）球腔中的自由热对流

板块运动是地幔对流的主要证据之一．同时，作为地球动力系统中一个相对独立部分，板块自身的存在和运动对地幔内部物质的流动形态有巨大影响．地幔内部的流动由两部分组成：一是由内部非绝热温度差异造成的自由对流解；另一部分是由在地表运动的板块所激发．作为系列工作的第一部分，本文研究球腔中的自由热对流问题．得到了对地幔对流研究有实际意义的下边界为自由、上边界为刚性情况下的临界瑞利数值，不同的瑞利数时球腔内流场和温度场的分布形态等．

COUPLING BETWEEN MANTLE CIRCULATION AND LITHOSPHERIC PLATES──（Ⅰ）THERMAL FREE CONVECTION IN A SPHERICAL SHELL

The motion of the lithospheric plates is one of evidences of convection in the mantle. On the other hand, as a relatively independent region of the Earth's dynamic system, the existence and motion of surface plates should have a substantial modify to mantle circulation. Probablely, the mantle flow is neither purely free convection genarated by buoyancy force nor forced convection excited by boundary force,but mixed convection which combines the effect of boundary and buoyancy forces.As the first part of successive research, in this paper we study thermal free convection in a spherical shell which constracts the base of the investigation of coupling between mantle convection and plate motions.In the case of inner boundary being stress-free and outer boundary being rigid, we obtaine the critical values of Rayleigh numbers which represent onset of instability and patterns of temperature and velocity field for different Rayleigh numbers.