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arXiv physics/0512180physics.geo-ph
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三维球壳中具有强烈温度和深度依赖粘性的低度地幔对流

Low-degree mantle convection with strongly temperature- and depth-dependent viscosity in a three-dimensional spherical shell

Masaki Yoshida, Akira Kageyama

摘要:

利用数值模拟方法,对三维球壳中无限普朗特数、瑞利数$10^7$和粘性随温度和深度变化的Boussinesq流体的热对流进行了研究,研究了没有类地板块构造的单板块类地行星(如金星或火星)的地幔对流.粘性随温度变化很大(沿壳层的粘性差为$\geq 10^5$),使得在滞盖结构下的对流为短波长结构。由于盖底部产生的次级下降流,形成了大量的圆柱形上升流。这种对流模式与金星或火星测地线观测所推断的对流模式不一致。研究了上地幔和下地幔层结粘度(粘度差在30 ~ 300之间)的附加效应。结果表明,强烈的温度和深度依赖性的粘度的组合导致长波长的对流结构,其中球谐度$\ell$是占主导地位的在1- 4。模拟计算的大地水准面异常具有长波长结构,并与观测结果进行了比较。当粘度随深度增加时,在30 ~ 100的较宽粘度差范围内,实现了与火星地幔相似的一级($\ell = 1$)对流。

英文摘要:

A series of numerical simulations of thermal convection of Boussinesq fluid with infinite Prandtl number, with Rayleigh number $10^7$, and with the strongly temperature- and depth- dependent viscosity in a three-dimensional spherical shell is carried out to study the mantle convection of single-plate terrestrial planets like Venus or Mars without an Earth-like plate tectonics. The strongly temperature-dependent viscosity (the viscosity contrast across the shell is $\geq 10^5$) make the convection under stagnant-lid short-wavelength structures. Numerous, cylindrical upwelling plumes are developed because of the secondary downwelling plumes arising from the bottom of lid. This convection pattern is inconsistent with that inferred from the geodesic observation of the Venus or Mars. Additional effect of the stratified viscosity at the upper/lower mantle (the viscosity contrast is varied from 30 to 300) are investigated. It is found that the combination of the strongly temperature- and depth-dependent viscosity causes long-wavelength structures of convection in which the spherical harmonic degree $\ell$ is dominant at 1--4. The geoid anomaly calculated by the simulated convections shows a long-wavelength structure, which is compared with observations. The degree-one ($\ell = 1$) convection like the Martian mantle is realized in the wide range of viscosity contrast from 30 to 100 when the viscosity is continuously increased with depth at the lower mantle.

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