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  • 1
    ISSN: 1610-2924
    Keywords: Fractal ; Heterogeneity ; Mantle convection ; Mixing ; Non-Newtonian rheology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract We analyzed and compared the mixing properties of 2-D mantle convection models. Two rheologically different models, Newtonian and non-Newtonian (power-law), were considered with both the line and field methods. The line method is based on monitoring of passive particles joined into lines, while the field method relies on the advection of a passive scalar field. Both visual and quantitative estimates revealed that the efficiency of the Newtonian mixing is greater than the non-Newtonian. A heterogeneity placed in the non-Newtonian convection forms horizontal structures, which may persist for at least 1 Ga on the upper-mantle scale. In addition, the non-Newtonian medium reveals a lesser amount of stretching of the lines than the Newtonian material. The rate of the Newtonian stretching fits well with an exponential dependence with time, while the non-Newtonian rheology shows the stretching rate close to a power-law dependence with time. In the Newtonian medium the heterogeneity is reorganized into two unstable vertical columns, while the non-Newtonian mixing favors horizontal structures. In the latter case, these structures are sufficiently stable in both the temporal and spatial planes to explain the mantle geochemical and geophysical heterogeneities. Due to the non-linear character of power-law rheology, the non-Newtonian medium offers a “natural” scale-dependent resistance to deformation, which prevents efficient mixing at the intermediate length scales.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1610-2924
    Keywords: Geophysics ; Numerical modelling ; Visualization ; Language ; Convection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract It was known that deep within numbers and binary data from simulations of geophysical convective flows resided various patterns. Two models of convective fluid flows were being considered. One was a model of two-dimensional (768 × 256) air convection with finite Prandtl number of one and Rayleigh number of 108−1010, and another was a model of three-dimensional (up to 120 × 120 × 90) mantle convection with infinite Prandtl number and Rayleigh number of 106−108. Clearly, phenomena existed which superceded each individual dimensionless computer model to provide a piece of information regarding actual fluid flows. The problem was how to find, prove, and communicate these patterns and phenomena for convection simulations with gigabytes of data. In a search for such an analytical and communicative tool, the alternative of visualization was considered. The need for visualization was recognized and discussed. Then, utilizing both two- and three-dimensional models of high Rayleigh number convection, basic techniques of style and content were developed. Applications of the visualization techniques were designed utilizing IBM’s Data Explorer in order to create communicative images and movies, and after the applications, the problems of data storage and transfer became apparent. Throughout the process though, it became clear how important the language of vision actually could be in the geophysics community. In a field in which words such as plumes and internal waves have in ways replaced mathematics as the basic language for science, there is a need for another resource, another language-the visualization of convective fluid flows.
    Type of Medium: Electronic Resource
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