Mathematical Sciences: Study of Strongly Chaotic Thermal Convection in the Earth's Mantle: Analytical, Computational and Visualization Perspectives
数学科学:地幔中的强混沌热对流研究:分析、计算和可视化视角
基本信息
- 批准号:9201042
- 负责人:
- 金额:$ 4万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:1993
- 资助国家:美国
- 起止时间:1993-07-15 至 1996-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The main thrust of this collaborative effort between applied mathematics (fluid dynamics) and geophysics (geophysical Fluid dynamics) is a focussed study of strongly chaotic three-dimensional convection as applied to the Earth's mantle, using analytical, numerical and visualization techniques. The investigator and his colleague David Yuen extend the usual canonical formulation of constant property simulation to include realistic depth-dependent thermal expansivity and viscosity thermal conductivity along with multiple internal phase transitions and internal heat generation. The presence of a triple point in the phase diagram and a more accurate temperature-dependent viscosity are also incorporated into the mathematical formulation. The investigators use the newly developed proper orthogonal decomposition (POD) and linear stochastic estimation (LSE) techniques to compress the enormous amount of data resulting from large-scale three-dimensional numerical simulations. The POD and LSE techniques are also used to characterize and understand the spatio-temporal dynamics of the relevant coherent structures, such as hot rising thermal plumes and cold sinking sheets. The investigators study relevant geophysical problems such as the underlying causes of large-scale circulation in the mantle, the relative stationarity of upwellings from depth-dependent material properties, gravitational instabilities caused by multiple phase transitions and the effect of temperature dependent viscosity on the mantle dynamics. They also conduct simulations with an imposed time-dependent boundary condition at the bottom to account for the cooling of the core, in order to study the thermal history by starting at very high Rayleigh number, like 10**8, and slowly lowering the Rayleigh number via cooling. The investigators use modern mathematical theories and numerical techniques to study the three-dimensional dynamics of the Earth's interior. An important issue arising in the last year is the possibility for gravitational instabilities to develop in the mantle due to phase transitions. This instability results in periodic eruption of superplumes and associated intense volcanic activity. The collaborators are among the first groups to model this phenomenon in three dimensions. They plan to study this further by incorporating more realistic flow laws and thermodynamics. There are still many aspects in this phenomenon of gravitational instability to explore, as increasing evidence from the correlation between past trench sites and the cold anomalies in the lower mantle, inferred from seismic tomography, suggests that such mantle instabilities could have occurred in the past 100 million years. Recognition of these instabilities may change traditional views of the role of steady-state processes. They also investigate the nature of coherent large-scale flow structures in the lower mantle as revealed by seismology, and what effects these instabilities have on the long-term thermal evolution of the Earth and Earth-like planets. It was only a few years ago that the idea of a thermal attractor from the collisions of plumes was introduced in geophysics. They expect that work on large-scale coherent structures maintained dynamically by mantle convection may also affect traditional views of geophysical behavior.
应用数学(流体动力学)和地球物理(地球物理流体动力学)之间的合作努力的主要推力是利用分析、数值和可视化技术,对应用于地幔的强混沌三维对流进行集中研究。研究者和他的同事David Yuen扩展了通常的恒定性质模拟的标准公式,以包括实际的深度相关的热膨胀率和粘度导热率,以及多个内部相变和内部热生成。相图中三相点的存在和更精确的温度依赖粘度也被纳入数学公式。研究人员使用新开发的正交分解(POD)和线性随机估计(LSE)技术来压缩大规模三维数值模拟产生的大量数据。POD和LSE技术还用于表征和理解相关相干结构的时空动力学,如热上升热羽流和冷下沉板。研究人员研究了相关的地球物理问题,如地幔大规模环流的根本原因、依赖于深度的物质性质、多重相变引起的引力不稳定性以及依赖于温度的粘度对地幔动力学的影响。为了研究热历史,他们还在底部施加了与时间相关的边界条件,以解释核心的冷却,以便从非常高的瑞利数开始,如10**8,并通过冷却慢慢降低瑞利数。研究人员使用现代数学理论和数值技术来研究地球内部的三维动力学。去年出现的一个重要问题是由于相变在地幔中产生引力不稳定性的可能性。这种不稳定性导致超级羽流的周期性喷发和相关的强烈火山活动。合作者是第一批在三维空间中模拟这种现象的团队之一。他们计划通过结合更现实的流动定律和热力学来进一步研究这个问题。这种重力不稳定现象还有很多方面需要探索,因为从地震层析成像推断出的过去海沟位置与下地幔寒冷异常之间的相关性越来越多的证据表明,这种地幔不稳定可能发生在过去的1亿年里。认识到这些不稳定性可能会改变对稳态过程作用的传统看法。他们还研究了地震学揭示的下地幔中连贯的大规模流动结构的性质,以及这些不稳定性对地球和类地行星长期热演化的影响。仅仅在几年前,从羽流碰撞中产生热吸引子的想法才被引入地球物理学。他们预计,对地幔对流动态维持的大尺度相干结构的研究也可能影响地球物理行为的传统观点。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Sivaramakrishna Balachandar其他文献
Sivaramakrishna Balachandar的其他文献
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