Magneto-convection in planets and stars

The existence of planetary and stellar magnetic fields is often attributed to the dynamo instability, which is caused by the motion of an electrically conducting fluid that amplifies a seed of magnetic field by induction. Despite nearly one hundred years of research, several questions remain open about the dynamics of planetary and stellar magnetic fields. Recent observation show that the magnetic field becomes weaker in certain geographical regions resulting in potential hazards, such as disruption to power grids, damage to satellites, etc. Thus, accurate modelling is urgently required to predict the dynamical behavior of the geomagnetic field.

The majority of studies so far consider the electrical conductivity of the fluid as a constant, which is a very crude simplification. For example, the liquid core of the Earth is driven by convection and the temperature, the chemical composition and the density of the fluid are all expected to display large variations. As a result, neither the thermal diffusivity nor the electrical conductivity of the fluid is unlikely to remain uniform in the bulk of the flow. Such considerations will change the whole picture we have so far for the dynamics of such flows.

Our aim is to consider the fluctuations of the thermal diffusivity and electrical conductivity due to their temperature dependence and study their effect on the dynamics of convection and the dynamo, respectively. Non-linear feedback from the magnetic field on the flow will also be considered to study the saturation mechanism(s) of the magnetic field.

Hydrodynamic instabilities have been studied for more than a century and are well documented experimentally as well as theoretically. The dynamo instability however occurs when a control parameter is varied within the turbulent regime and theoretical tools are lacking to handle such instabilities. The novelty of our research methodology lies in the development of new mathematical connection with tools from critical phenomena and phase transitions to understand better these kind of instabilities that occur on a turbulent background flow. Moreover, the behavior of the dynamics in certain limits will be tackled using advanced asymptotic methods in conjunction with high fidelity numerical computations. One of the important outcomes of this work will be the development of simplified dynamical descriptions of the system. These reduced dynamical systems will capture the key physics of these flows, and provide a generic tool for understanding and modelling their dynamics.

This project falls within the EPSRC research areas of continuum mechanics and non-linear systems.