Complete measurement of helicity and its dynamics in vortex tubes

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Science  04 Aug 2017:
Vol. 357, Issue 6350, pp. 487-491
DOI: 10.1126/science.aam6897

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Linking fluids as they twist and writhe

Helicity is a measure of cork-screw-like motion described by the amount of twisting, writhing, and linking in a fluid. Total helicity is conserved for ideal fluids, but how helicity changes in real fluids with even tiny amounts of viscosity has been an open question. Scheeler et al. provide a complete measurement of total helicity in a real fluid by using a set of hydrofoils to track linking, twisting, and writhing (see the Perspective by Moffatt). They show that twisting dissipates total helicity, whereas writhing and linking conserve it. This provides a fundamental insight into tornadogenesis, atmospheric flows, and the formation of turbulence.

Science, this issue p. 487; see also p. 448


Helicity, a topological measure of the intertwining of vortices in a fluid flow, is a conserved quantity in inviscid fluids but can be dissipated by viscosity in real flows. Despite its relevance across a range of flows, helicity in real fluids remains poorly understood because the entire quantity is challenging to measure. We measured the total helicity of thin-core vortex tubes in water. For helical vortices that are stretched or compressed by a second vortex, we found conservation of total helicity. For an isolated helical vortex, we observed evolution toward and maintenance of a constant helicity state after the dissipation of twist helicity by viscosity. Our results show that helicity can remain constant even in a viscous fluid and provide an improved basis for understanding and manipulating helicity in real flows.

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