Dr. Michael A. Calkins has been awarded an NSF Earth Sciences Postdoctoral Fellowship to carry out a research and education plan at the University of Colorado, Boulder. This investigation will employ computationally efficient two-dimensional numerical simulations to improve our understanding of thermochemical convection dynamics in the Earth's liquid outer core. The goal of this work is to determine how the dynamics of the core change when both thermal and chemical buoyancy are present, the sensitivity of the resulting flow to the value of the thermal and chemical diffusivities, and how the dynamics have changed over time in response to the slow cooling of the Earth. The results will be fundamental for helping to understand the structure of the Earth's magnetic field and the dynamo process by which it is maintained.
It is widely believed that the Earth's magnetic field is generated by fluid motion in the molten iron outer core. However, this "dynamo" process remains one of the least understood phenomena in the Earth sciences. This project will use computer simulations to investigate the fluid motions within the core. The research will be crucial for improving our understanding of the dynamo mechanism and the evolution of the core. Furthermore, the results will be broadly applicable to other areas of the Earth sciences where similar fluid motions occur, such as the Earth's mantle, oceans, and magma chambers. Dr. Calkins will engage a diverse body of undergraduate and graduate students in the mathematical and physical sciences by teaching a semester-long course on modeling fluid motion in the Earth sciences. The goal of the course is for each student to design and run a computational fluid dynamics code on multi-processor machines. Students will learn the fundamental skills required to understand and model the fluid flow phenomena that are ubiquitous in the Earth sciences.
It is now well accepted that the Earth's magnetic field is sustained by turbulent motions within the molten iron outer core. However, advancing our understanding of this system is made difficult due to observational limitations. Theory and modeling must fill the observational gap in order that our understanding of the Earth's core and magnetic field is improved. While the equations governing the fluid motions and magnetic field of the core are well known, they are intrinsically difficult to solve; similar difficulties are associated with investigations of the Earth's atmosphere and ocean. Solving such equations with realistic parameters on large computers has proven elusive due to technological constraints. Therefore, this project's primary focus has been on employing rigorous mathematical methods for the purpose of simplifying the governing equations by focusing only on those spatial and temporal scales that are of dynamical interest. A new, more accurate model has been developed during the course of the award and computer simulations of the model are currently being carried out. In addition, the numerical strategies that have been developed represent a significant step forward in terms of efficiency, and so can be employed in many existing models to allow for a more accurate representation of the dynamics within Earth's core. This project has resulted in the use and development of two separate mathematical techniques that can be used for a wide variety of problems. The first is the use of multi-scale asymptotics; this method is used to exploit the disparate time and space scales, as well as spatial anisotropies that are often present in many systems. Through the rigorous use of such methods, governing equations can be greatly simplified by removing time and space scales that are not of scientific interest for a given problem. The resulting equations often make for a more intuitive and straightforward interpretation of observed dynamics in such problems. Given these significant advantages, however, the "reduced" equations are often not written so simply that closed-form analytical solutions can be obtained. It is therefore necessary to have recourse to numerical solutions of the governing equations, whereby the solution is obtained only as numerical output. A computational strategy for solving equations was developed over the course of the project that is significantly more efficient than existing methods. This technique is not limited to the specific problem under consideration and so can be employed to a broad variety of problems requiring numerical solutions to governing equations. Thus, by employing the methods developed over the project period, many of the problems in parallel fields should be more easily analyzed, highlighting the broad utility of the results of this project.
