## Model reduction and direct statistical simulation in fluids

The development of statistical theory for turbulent flows has often focussed on the homogeneous and isotropic case. In many systems of interest, the underlying fluid is far away from this paradigm beloved by theoreticians. For example, mean flows, rotation, and stratification may play a role in introducing inhomogeneity and anisotropy. In this talk, I shall introduce the concept of Direct Statistical Simulation (DSS) of turbulent flows as one form of model reduction. I shall give examples of its effectiveness in problems such as the generation of zonal flows in planets and the interaction of shear flows and magnetic fields in stably stratified stars. Such a procedure could be useful for subgrid modelling of turbulent flows; however, this method is subject to the "curse of dimensionality" and so methods that are able to reduce the required basis are necessary. Some success has been achieved in "learning the optimal basis" by hand, and it seems as though this method is ripe for advances through machine learning.

*Steven Tobias is a Professor of Applied Mathematics at the University of Leeds. Previous to coming to Leeds he was a Research Fellow in Mathematics at Trinity College Cambridge (1995-2000) and a Research Associate at JILA, University of Colorado (1996-1998). His Ph.D. (1995) was on "Solar and Stellar Dynamos" at DAMTP, the University of Cambridge under the supervision of Professor Nigel Weiss (FRS). Tobias is currently Director of The Leeds Institute of Fluid Dynamics. https://fluids.leeds.ac.uk/ His research covers fluid dynamics with particular emphasis on Geophysical and Astrophysical Fluid Dynamics...from turbulence in the Earth's oceans and atmosphere to the interaction of magnetic fields and plasmas in tokamaks, experiments, planets, stars, and accretion disks.*