Scales of mantle heterogeneity from 3D numerical models of mixing

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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.