Dynamics of the Earth’s core from spherical dynamo models

Faculty: Binod Sreenivasan (CES) and Arnab Rai Choudhuri (Physics)

The magnetic field of Earth and other planets is thought to be generated by dynamo action in their fluid cores. Numerical simulations of the geodynamo performed on massively parallel computers have successfully captured several observable features of the geomagnetic field such as its large-scale axial dipole structure, high-latitude magnetic flux concentrations and occasional polarity reversals. Research performed at the Centre for Earth Sciences, IISc focuses on building Earth-like numerical dynamo models. The structure of convection in the core, which in turn gives rise to the observed geomagnetic field, is of particular interest. Flow in the Earth’s core is determined by several factors such as the basic state temperature profile, the planet’s background rotation, lateral heat flux variations at the core-mantle boundary (CMB) and the self-generated magnetic field. Whereas three-dimensional dynamo simulations attempt to capture the combined effect of all these factors, understanding their individual roles in isolation requires simpler linear models. A popular example is that of Rayleigh-Benard convection in a rotating plane layer with an imposed magnetic field. The effects of different buoyancy profiles and magnetic fields can be understood from such models. Lateral inhomogeneites at the CMB can be studied only through bi-global models, where all variables vary in 2 directions. These problems are more complex to set up mathematically and their numerical solution is memory-intensive; nevertheless they are simpler to interpret than 3D dynamo simulations. The proposed PhD project will aim to set up linear bi-global magneto-convection models for the Earth’s core and compare them with 3D simulations of the geodynamo.

Geodynamo simulations involve simultaneous solutions of the momentum, heat (or composition) and magnetic induction equations in spherical shell geometry. The computations are often massively parallel, and the numerically accessible dimensionless parameter regime is far from that thought to exist in the Earth’s core. The magnetic field strength obtained in these models compares well with the observed field strength in the Earth, which has provided the motivation to refine dynamo models with more “Earth-like” parameters. Rapid rotation makes the time step very small in the dynamo code, and will likely produce small-scale flows and large-scale dipole-dominated magnetic fields. This scale-separation between the velocity and magnetic fields is believed to exist in the Earth’s core, but is yet to emerge from dynamo simulations.

The PhD student should have a good mathematical and computational background. Knowledge of spherical harmonic expansions and numerical solutions of PDEs will be an advantage. The student will use the in-house dynamo code developed by Dr Sreenivasan, presently set up on the local computing cluster at the Centre for Earth Sciences as well as on the new CRAY XC40 supercomputer in SERC, IISc.