球层中高阶自由热对流格局及其变化的研究.PDFVIP

球层中高阶自由热对流格局及其变化的研究 朱 涛 冯 锐 （中国地震局地球物理研究所，北京，100081） 摘要：研究了下边界为应力自由边界，上边界为刚性边界，纯粹从底部加热的充满了无穷大普朗特数 的 Boussinesq 流体的同心球层中的非线性自由热对流。借鉴将极型场和扰动温度场展成勒让德多项式（以 下称零级数模型，即此时 m = 0）的方法，本文将它们展成 6 阶 6 级（即 l = 6, m = 0,1,2,…,l）的勒让德函 数（以下称高级数模型），并用 Garlekin 方法求解非线性方程组，获得了高级数模型的结果。与零级数模 型仅能获得表征物质垂直运移特征和扰动温度结构的二维南北向（r-θ ）剖面相比，高级数模型还得到了 东西向（r-?）和深度剖面（θ -?），而且对流运动的许多细特征得以体现，有利于深化认识球层中自由热对 流的特征及其导致的温度结构。瑞利数的大小对自由热对流的格局和速率产生了重要的影响，控制着对流 层中高温热柱区和低温冷柱区的相对大小。本文所得到的结果可能主要反映了下地幔物质运动，其对流格 局和速率在不同的位置上存在明显的差异可能蕴涵了重要的地球动力学含义。 关键词：非线性热对流 常粘度 Garlekin 方法 Article ID: 1000-9116(2004)06-0000-15 The patterns of high-degree thermal free convection and its ? features in a spherical shell ZHU Tao (朱 涛)???? FENG Rui (冯 锐) Institute of Geophysics, China Earthquake Administration, Beijing 100081, China Abstract：A high-degree (degree l = 6 and order m = 0, 1, 2, L, l. High-order model for short) and steady thermal free convective motion of an infinite Prandtl number and Boussinesq fluid in a spherical shell is calculated by a Galerkin method. Convection is driven by an imposed temperature drop across top rigid and bottom stress-free isothermal boundaries only heated from below of the shell. In this paper, the scalar poloidal and fluctuating temperature fields are expanded into associated Legendre polynomials with degree l= 6 and order m = 0, 1, 2, L, l. Compared with zero-order model (degree l= 6 and order m= 0), from which 2-D longitudinal (r?θ ) profiles can be obtained, high-order model can provide a series of southerly (r?θ ), easterly (r??) and radial (θ ??) velocity pr