We have made progress on the following:
1) We have been investigating convection in geometries relevant to rapidly rotating planets and stars. My team member Sandeep Kanuganti has managed to formulate the problem in both a three-dimensional annulus and in a geometry relevant to experiments to be performed at UCLA by Professor Jon Aurnou.
2) Together with team members Kuan Li and Girish Nivarti, I have been investigating Direct Statistical Simulation in both ODE and PDE models. Excellent progress has been made leading to many publications and some that are to appear in the next couple of years.
3) We have been developing timestepping methods for slow-fast dynamics relevant to rapidly rotating astrophysical objects. In addition we have been investigating rotating magnetoconvection.
4) Together with team member Pallavi Bhat, I have been investigating the role of magnetic helicity in computational models of dynamo action. This has led to a publication in preparation.
5) Together with team member Curtis Saxton, I have been investigating the effectiveness of the quasilinear and generalised quasilinear approximations for models of convection. This has led to a couple of publications and significant theoretical developments.
6) Together with team member Curtis Saxton, I have been investigating theoretically and mathematically the interactions involved in the generalised quasilinear approximation.
7) Together with team member Curtis Saxton, I have been investigating, the use of logarithmic lattices in problems of astrophysical flows.
8) Together with team member Anna Guseva, we have examined the use of data-driven methods for producing reduced order models of astrophysical flows.
9) Ankan Banerjee, Calum Skene and I have been looking at utilising Fourier Neural Operators (a form of machine learning) to solve the relevant equations for the generation of zonal flows in planets and stars. This promises some significant success.
The project has been extremely successful, leading to (so far) over 30 research papers and development of the field and of numerical techniques that can be utilised by the whole community. Many thanks have been given at international conferences and workshops.
