液核自由运动的变分方法

从流体静力平衡地球的弹性-引力运动动量方程出发，以角动 量方程控制弹性地幔、液态外核和弹性内核之间的相对转动，在球对称近似下考虑了地幔和 内核对液核边界扰动的形变响应，并以此作为液核边界运动的约束条件．根据地球简正模对 称性的一般特征，建立了自转、非黏性、椭球分层流体外核自由振荡运动的变分原理并给出 了相应的泛函．

Variational Approach to Free Motion in the Earth's Fluid Outer Core

This study is based on the elasto gravita t ional motion equations for a hydrostatic equilibrium Earth. The relative rotatio n among the solid elastic mantle, the fluid outer core and the solid elastic inn er core is governed by the angular momentum equation. The deformation response o f the mantle and inner core to the core dynamics, generated by the perturbations on the boundaries of the fluid outer core, is considered on the assumption of t he spherical symmetry. This response is employed to constrain the movement on th e boundaries of the fluid outer core. Based on the general symmetrical character istics of the Earth’s eigenmodes, the variational principle of free oscillation s in a rotating, inviscid and elliptically stratified fluid outer core is develo ped and the corresponding functional is deduced.