222. Moffatt, H. K. 2021b Some topological aspects of fluid dynamics. J. Fluid Mech. 914, P1,1- P1,56.

This 'Perspectives' paper in JFM surveyed many issues in fluid mechanics that have a topological character:  flows with boundary singularities, Lagrangian chaos, frozen-in fields, magnetohydrodynamic analogies, fast- and slow-dynamo mechanisms, magnetic relaxation, minimum-energy states, knotted flux tubes, vortex reconnection and the finite-time singularity problem. 

This picture illustrates relaxation of two magnetic flux tubes 'tied' at perfectly conducting boundaries.  Under 'ideal' conditions, a current sheet forms where the tubes make contact, but nonzero resistivity will inevitably cause diffusive tube reconnection. 

Braid tightening.png

224. Moffatt, H.K., Guest, H. & Huppert, H. E. 2021 Spreading or contraction of viscous drops between plates: single, multiple or annular drops. J. Fluid Mech. 925, A26.

Screenshot 2021-12-08 at 10.28.29.png

When a drop of viscous fluid (here treacle!) is placed between two horizontal glass plates, the upper plate being allowed to descend under its own weight, the drop expands, forming a nearly perfect circle; the radius actually increases as t^{⅛} - the 'one-eighth power law'. 

If the plates are then gradually levered apart from one corner, an intricate `fingering` pattern spreads across the drop from the point of leverage, sometimes preceded by cavitation bubbles where the pressure is very low.

Fingering.png

This type of experiment can be easily demonstrated in lectures, provided an old-fashioned overhead transparency projector is available. Fingering is a generic phenomenon when a fluid (here air) is caused to penetrate a more viscous fluid (here the treacle). This is a significant complication in many applications ranging from adhesion to oil recovery to carbon sequestration.