This research addresses the dynamics of the Earth¹s mantle in order to provide insight into sources and scales of heterogeneity and the long-term evolution of the Earth¹s deep interior and its influence on geological processes. We use a new implementation of a method for computing the stretching and thinning of ellipsoidal tracers in three orthogonal directions in isoviscous, incompressible three-dimensional flows, combined with new methods for visualizing 3D convection and mixing to identify stationary points, closed paths, and other features, found within the complex, 3D data generated by mantle convection models. These methods are to be implemented in established mantle convection codes to construct and then analyze time-varying mantle models with a large number of particles. The research addresses three fundamental topics: (1) the rate of mixing 3D time-dependent convection in the mantle, and the formation and destruction of structural patterns that can lead to the observed scales of heterogeneity (2) the structure and dynamics of mixing in boundary layers, especially in the lower mantle¹s D² layer and (3) the mixing associated with mantle plumes.
One of the fundamental open questions in dynamics of Earth¹s deep interior concerns the scales of the observed heterogeneity in the mantle. The development, and destruction, of heterogeneity by mantle convection reflects the long-term history and thermal evolution of the Earth as a planet. To determine the origins, evolution, and persistence of heterogeneity in the mantle requires understanding the physics of mixing by mantle convection. This problem has long been a topic of study, but it has not been resolved because scientists lacked the means to fully characterize mixing in 3D. Our research addresses this question by developing the computational methods to study mixing in 3D and applying these methods to numerical simulations of mantle convection. The results will enable improved interpretation of the observed seismic and geochemical observations of anisotropy and heterogeneity in the mantle. In the course of the research, we will develop and implement new methods for modeling mixing in viscous fluids, an important area of research across multiple disciplines, and for flow visualization. The methods developed will be applicable to computational fluid dynamics research in engineering as well as having applications to geophysics.
Overview: The motivation for this research is to understand the physical processes driving long term evolution of the Earth’s mantle, by using numerical models of mantle convection informed by geochemical observations of the mantle’s heterogeneity. Specifically, this project developed, tested, and implemented numerical methods for quantifying mixing in computer models of convection in a viscous fluid, applying these methods to address the origins, persistence, and structure of geochemical heterogeneities in the Earth’s mantle. Mixing is a fundamental process of convection; heterogeneities are created by the processes inherent in the plate tectonic cycle, including melting at mid-ocean ridges, formation of the continental crust, and subduction. The heterogeneities formed by plate tectonics are gradually destroyed by the stretching and folding action of convection. Because mantle convection is not accessible to direct observation, the information provided by mantle heterogeneity is a key to understanding the evolution of Earth’s interior. Our findings indicate that mantle mixing is a complex but relatively efficient process. Because the pattern of mantle convection changes through geologic time, mixing is controlled by the length of time that a parcel of mantle spends in regions of rapid stretching and folding. We further concluded that the mantle likely contains a deep reservoir that has persisted through geological time, though its structure has evolved in response to changes in plate configuration. Intellectual merits: In this project, we developed a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows and applied it to kinematic and dynamical models of flows designed to simulate mantle convection. We also used tracer particle methods to investigate 3D mixing in convection in a self-gravitating spherical shell. This involves introducing passive markers, tracking their position, and evaluating the distribution in space and time that results from the models. The physics of mixing is a subject of research in fluid dynamics and engineering, so new methods of modeling mixing can have impacts beyond the field of solid earth research. We have implemented the tracers into two open source codes used by the geophysics research and education community to model mantle convection. We also investigated the implications of mantle mixing for scenarios for the evolution of the mantle, informed by both mantle mixing and plate tectonics reconstruction. Broader Impacts This work and its results contribute to a general understanding of mixing in complex flows, and to the effectiveness, accuracy, and performance of different computational approaches for simulating mixing. Because the model outputs are difficult to visualize, we have been collaborating with computer scientists with expertise in computer graphics and scientific visualization to explore methods for conveying the results visually. The research used and contributed to development of open source codes that are widely used by the mantle convection community. The project involved undergraduate students, graduate students, and postdoctoral scholars in research, and helped prepare them for careers that involve developing and using advanced computational methods. Students involved in this project had the opportunity to collaborate with visiting international computer science students, postdoctoral scholars, and faculty. We worked with science museums to provide visualization products for informal science education.
