The geometry of Lagrangian averaging in fluids

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• Jacques Vanneste, University of Edinburgh
• Thursday 07 March 2019, 12:00-13:00
• PHYW-LT (117).

If you have a question about this talk, please contact Fabian Spill.

Many fluid models are derived by averaging the equations of motion to obtain coarse-grained representations of small-scale processes (fast waves, subgrid turbulence). It has long been realised that Lagrangian averaging, that is, averaging at fixed particle labels, has advantages over the more straightforward Eulerian averaging at fixed position, in particular in its handling of material conservations (of density or vorticity). This has led to the development of the now well-established generalised Lagrangian mean theory. In this talk, I will describe how taking a geometric, coordinate-free viewpoint helps uncover the structures underlying this theory and fix some of its weaknesses. The treatment emphasises the arbitrariness in the definition of the mean flow and introduces a new definition based on least-squares in the group of diffeomorphisms. (Joint work with A D Gilbert, Exeter.)

This talk is part of the Applied Mathematics Seminar Series series.

This talk is included in these lists:

• Applied Mathematics Seminar Series
• PHYW-LT (117)
• School of Mathematics Events

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