The Earth's magnetic field is now known to be the result of fluid motion within the Earth's molten iron outer core. This "dynamo" process remains one of the least understood phenomena in the Earth sciences, however, due to the lack of direct observations. Computer simulations have proven to be valuable tools for advancing our understanding of dynamos. Nevertheless, it is not currently possible to capture all the temporal and spatial scales of dynamical relevance in the Earth's core given modern-day technological constraints. The PIs are overcoming these limitations by developing the first multi-scale mathematical model of the geodynamo. In this respect, the proposed work can be viewed as a new computational and modeling framework that will allow for the highest resolution simulations of the Earth's core to date. Additionally, these methods will be broadly applicable to a range of other scientific problems ranging from molecular physics to cellular dynamics.
Three-dimensional numerical simulations have vastly improved our understanding of convection driven dynamos, yet computational constraints currently limit them to physical parameters that are distant from those that characterize the Earth's liquid outer core. This fact highlights a serious gap in our understanding of the geodynamo, and severely limits our ability to relate directly geomagnetic field observations and the output of numerical dynamo models. The proposed work will, for the first time, employ the methodology of multiple scale asymptotics to planetary dynamo systems for purpose of developing a model that is capable of reaching parameter values and physical properties of Earth's core. In this way, the asymptotic regime of the proposed model will provide a more complete understanding of geomagnetic field observations. Findings of the research will be directly applicable to other rapidly rotating, turbulent fluid systems on and within stars, extrasolar planets, and the other planets within the Solar System. Moreover, the mathematical methods employed for development of the reduced equations are broadly applicable to a range of other scientific problems ranging from molecular physics to cellular dynamics.
