Direct Statistical Simulation of Mulitscale Fluids

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.

This research is to be carried out in the Astrophysical and Geophysical Fluid Dynamics research group, which is one of the largest such research groups in the world.