This summer I published an article in Science, together with Prof. William Irvine and his group at the University of Chicago, discussing our results on the dynamics of helicity in a viscous fluid. Helicity is a scalar quantity that measures the intertwining of vortex lines in a fluid domain. In ideal (inviscid) fluids, helicity is conserved – but in viscous fluids helicity can increase, decrease, or (as we showed) stay the same.

A set of helical vortex loops generally has helicity contributions from twist, linking, and writhe. Source

The first major contribution was an experimental break-through by the Chicago group: we introduced a new technique to measure helicity in a real fluid, water, for the special case of thin-core vortices. The total helicity for such vortices can be split into two components: the writhe, or ‘curling’ of the vortex centerline, and the twist of the vortex lines that are swirling around the centerline. The writhe can be computed just by inspecting the geometry, or shape, of the centerline, and together with the measurement of total helicity we could compute the twist by subtracting one from the other.

This provided our second major contribution: by observing the dynamics of twist and writhe separately, and using some theoretical analysis, we could show that for our helical vortex loops, the twist contribution would always be dissipated by viscosity, whereas the writhe of the centerline persists. This means the an initial helical vortex loop, with both twist and writhe, will see its twist being dissipated by viscosity and end up as a twist-free, writhing vortex that persists. In other words: helicity can be non-zero and conserved, even in a viscous fluid.

This is just the beginning: looking at fluid flows through the lens of vortex-line geometry is a promising approach to study the flow evolution. There are many questions that are still unanswered, mostly relating to the dynamics of twist in helical vortices.

You can find the full article on our publications page, or click here to download the pdf. For more insight in this topic, Prof. H. Keith Moffatt wrote an insightful perspective on our article that can be found here.