关于安德拉德星球的爱情数字

IF 2.9 3区 地球科学 Q2 ASTRONOMY & ASTROPHYSICS
Anastasia Consorzi, Daniele Melini, Juan Luis González-Santander, Giorgio Spada
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引用次数: 0

摘要

安德拉德流变模型经常被用来描述太阳系或太阳系外行星对潮汐扰动的响应,特别是当它们的特性还没有得到很好的约束时。对于具有稳态麦克斯韦流变学的均匀行星,很早以前就确定了洛夫数的解析形式,但对于瞬态安德拉德流变学,目前还没有确定闭式解,行星响应通常是在频域进行半解析或在时域进行数值研究。闭式表达式具有潜在的重要性,因为它们可以让我们深入了解爱数与模型参数和行星等静态再调整的时间尺度之间的关系。首先,我们将重点放在一维的安德拉德流变定律上,并在时域上获得了之前未知的弛豫模量的显式表达式,该表达式是对指数函数进行概括的高阶米塔格-勒夫勒超越函数 Eα,β(z)。其次,我们考虑了不可压缩行星模型(通常称为 "开尔文球")的一般响应,通过分析方法研究了拉普拉斯域、频域和时域爱数。通过数值方法,我们评估了压缩性对拉普拉斯域和频域爱数值的影响。此外,利用在一维情况下获得的结果,我们建立了时域爱数的闭式(尽管不是基本的)表达式,并通过分析讨论了具有安德拉德流变学的开尔文球的频域响应。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

On the Love Numbers of an Andrade Planet

On the Love Numbers of an Andrade Planet

The Andrade rheological model is often employed to describe the response of solar system or extra-solar planets to tidal perturbations, especially when their properties are still poorly constrained. While for uniform planets with steady-state Maxwell rheology the analytical form of the Love numbers was established long ago, for the transient Andrade rheology no closed-form solutions have been yet determined, and the planetary response is usually studied either semi-analitically in the frequency domain or numerically in the time domain. Closed-form expressions are potentially important since they could provide insight into the dependence of Love numbers upon the model parameters and the time-scales of the isostatic readjustment of the planet. First, we focus on the Andrade rheological law in 1-D and we obtain a previously unknown explicit form, in the time domain, for the relaxation modulus in terms of the higher Mittag-Leffler transcendental function Eα,β(z) that generalizes the exponential function. Second, we consider the general response of an incompressible planetary model — often referred to as the “Kelvin sphere” — studying the Laplace domain, the frequency domain and the time domain Love numbers by analytical methods. Through a numerical approach, we assess the effect of compressibility on the Love numbers in the Laplace and frequency domains. Furthermore, exploiting the results obtained in the 1-D case, we establish closed-form — although not elementary — expressions of the time domain Love numbers and we discuss the frequency domain response of the Kelvin sphere with Andrade rheology analytically.

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来源期刊
Earth and Space Science
Earth and Space Science Earth and Planetary Sciences-General Earth and Planetary Sciences
CiteScore
5.50
自引率
3.20%
发文量
285
审稿时长
19 weeks
期刊介绍: Marking AGU’s second new open access journal in the last 12 months, Earth and Space Science is the only journal that reflects the expansive range of science represented by AGU’s 62,000 members, including all of the Earth, planetary, and space sciences, and related fields in environmental science, geoengineering, space engineering, and biogeochemistry.
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