庞卡罗地球模型的旋转模式

IF 1.1 4区 地球科学 Q3 ASTRONOMY & ASTROPHYSICS
B. Seyed-Mahmoud, Y. Rogister
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引用次数: 3

摘要

本文首先利用一个具有均匀不可压缩液核(LC)和刚性地幔(MT)的简单地球模型,研究了poincar地球模型的以下旋转模式:倾斜模式(TOM)、自旋模式(SOM)和自由核章动(FCN)。我们得到了这些模态周期和钱德勒摆动周期的解析解。我们分析了TOM和SOM之间的区别,并且FCN确实与摆动地球的SOM相同。我们用减压作为自变量,矢量动量方程可以用减压来简化为标量二阶偏微分方程,称为庞加莱方程。然后找到了上述模态在液芯子午平面上的位移特征函数的解析解。接下来,我们考虑一个类似于上面的三层地球模型,其中也包括一个刚性内核(IC)。我们首先证明了如果IC锁定在MT上,CW的周期函数和特征函数存在解析解,即它们具有相同的摆动运动。我们证明这是重要的,因为它表明连续波在庞卡罗(不可压缩和无粘性LC)摆动的地球模型中表现出来。我们进一步允许内核独立摆动,并数值计算TOM、SOM和FCN的周期和位移特征函数,以及另一种旋转模式——内核摆动(ICW)的周期和位移特征函数。接下来,我们表明,在计算自由内核章动(FICN)的周期和特征函数时,内核截获的特征表面的存在可能是该模式收敛缓慢(或缺乏)的原因。最后,我们表明,尽管在使用Sasao近似求解ICW和FICN的频率时忽略了地幔的摆动运动,但这两种模式的解析解产生的周期几乎与文献中类似的地球模型的解析解相同,其中地幔也允许摆动。我们推断,Sasao的近似,或场变量、压力、重力势和位移矢量分量的级数解的严重截断,可能不足以准确描述在FICN激励期间液芯内的运动。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rotational modes of Poincaré Earth models
ABSTRACT We study the following rotational modes of Poincaré Earth models: the tilt-over mode (TOM), the spin-over mode (SOM) and free core nutation (FCN), using first a simple Earth model with a homogeneous and incompressible liquid core (LC) and a rigid mantle (MT). We obtain analytical solutions for the periods of these modes as well as that of the Chandler wobble (CW). We show analytically the distinction between the TOM and the SOM and that the FCN is indeed the same mode as the SOM of a wobbling Earth. The reduced pressure, in terms of which the vector momentum equation is known to reduce to a scalar second-order partial differential equation called the Poincaré equation, is used as the independent variable. Analytical solutions are then found for the displacement eigenfunctions in a meridional plane of the liquid core for the aforementioned modes. We next consider a three-layer Earth model similar to above which also includes a rigid inner core (IC). We first show that analytical solutions exist for the period and eigenfunctions of the CW if the IC is locked to the MT, i.e. they have the same wobbling motion. We show that this is significant as it shows that the CW manifests itself for a Poincaré (incompressible and inviscid LC) wobbling Earth model. We further allow for the inner core to wobble independently and compute numerically the periods and displacement eigenfunctions of the TOM, SOM and FCN, as well as those for still another rotational mode, the inner-core wobble (ICW). Next we show that the presence of the characteristic surfaces intercepted by the inner-core, when computing the period and eigenfunctions of the free inner-core nutation (FICN), may be the reason for the slow (or lack of the) convergence of this mode. Finally, we show that even though the wobbling motion of the mantle is ignored when solving for the frequencies of the ICW and the FICN when Sasao's approximation is used, the analytical solutions for both these modes yield periods nearly identical to those in the literature for a similar Earth model with mantle allowed to wobble as well. We infer that the Sasao's approximation, or the severe truncation of the series solution of the field variables, the pressure, the gravitational potential and the components of the displacement vector, may not be adequate to accurately describe the motion in the liquid core during the excitation of the FICN.
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来源期刊
Geophysical and Astrophysical Fluid Dynamics
Geophysical and Astrophysical Fluid Dynamics 地学天文-地球化学与地球物理
CiteScore
3.10
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: Geophysical and Astrophysical Fluid Dynamics exists for the publication of original research papers and short communications, occasional survey articles and conference reports on the fluid mechanics of the earth and planets, including oceans, atmospheres and interiors, and the fluid mechanics of the sun, stars and other astrophysical objects. In addition, their magnetohydrodynamic behaviours are investigated. Experimental, theoretical and numerical studies of rotating, stratified and convecting fluids of general interest to geophysicists and astrophysicists appear. Properly interpreted observational results are also published.
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