Direct Statistical Simulation of Geophysical and Astrophysical Flows

This project is to implement the new technique of Direct Statistical Simulation for a range of Astrophysical and Geophysical Flows. Complicated fluid dynamical processes are often investigated using Direct Numerical Simulation of the underlying partial differential equations of fluid mechanics. Many techniques are available for solving for the dynamics of such systems efficiently. However these techniques are often prohibitively expensive for calculating statistics, which are usually the objects of interest in geophysics and astrophysics. In this project we shall develop and utilise the new technique of Direct Statistical Simulation (DSS) where the statistics of the flow are solved for directly using cumulant hierarchies. This novel technique has proven to be extremely efficient for problems with non-trivial mean behaviour and non-local interactions. However there is much to understand about this procedure, which makes it an ideal topic for a PhD.

As this technique is extremely general it can be applied to many problems of geophysical and astrophysical interest such as the formation of jets in planets and the oceans, differential rotation in stars, instabilities in stellar and planetary interiors and atmospheres and the dynamics of accretion disks and astrophysical dynamos.

The group is a leader in the field of Astrophysical and Geophysical Fluid Dynamics, with international reputation in dynamo theory, astrophysical MHD and convection. It's strength has been recognised by the award of several prizes and special fellowships and holds one of the largest grants ever awarded to the University of Leeds. The nine permanent members of staff work with eighteen postdocs and postgraduate students.

The group is actively engaged in research in a wide-range of areas of astrophysical and geophysical fluid dynamics: from planetary dynamics (the geodynamo and planetary dynamos) through solar, stellar and galactic dynamics to highly compressible and relativistic dynamics on the largest scales. Magnetic fields are a strong theme, and the group is interested in how planets (like the Earth), stars (like the Sun), neutron stars, black holes and galaxies generate their magnetic fields through dynamo action. On the Sun, the well-known eleven-year sunspot cycle is a manifestation of the solar dynamo; indeed the solar magnetic field underlies all solar magnetic phenomena such as solar flares, coronal mass ejections and the solar wind. In the Earth, magnetic fields are generated by convection in the molten iron core, and it has recently become possible to solve the fundamental equations that govern the motion of fluids and the generation of magnetic fields, and successfully reproduce many of the observed features of the geomagnetic field. At the other end of the scale, magnetic fields are implicated in the formation of spectacular jets coming from neutron stars, black holes and galaxies. Without magnetic fields, the group has interests in waves and hydrodynamic instabilities in rotating stratified fluids, with applications to the Earth's atmosphere and ocean (and with application to other planets).

keywords: applied mathematics, fluid dynamics, turbulence