Geometric fluid mechanics and generalised Lagrangian mean (GLM) theory

I will talk about how one can average the equations of fluid mechanics over fluid parcels in the well-known Generalised Lagrangian Mean (GLM) theory of Andrew and McIntyre (1978) and give a modern perspective on this using tools of differential geometry (though I will aim to make much of the talk accessible to those without too much knowledge in this area). (Joint work with Jacques Vanneste, University of Edinburgh).