PerspectiveApplied Physics

Helicity—invariant even in a viscous fluid

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Science  04 Aug 2017:
Vol. 357, Issue 6350, pp. 448-449
DOI: 10.1126/science.aao1428

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The vortex ring is a fundamental phenomenon of fluid dynamics, recognized since the seminal investigations of Helmholtz (1) and Kelvin (2). Its familiar manifestation as a “smoke ring” in air derives from the fact that both smoke and vorticity (local fluid spin) are transported with the flow, which is “induced” by the vortex itself; so the smoke provides a natural visualization of the vorticity (see the photo). Vortex rings can also be generated in water and visualized either by dye or by small air bubbles that migrate to the low-pressure region at the core of the vortex. On page 487 of this issue, Scheeler et al. (3) explore a particular property of a vortex ring whose core is helical rather than circular in form. This property, helicity, is an integral over the fluid domain that expresses the correlation between velocity and vorticity, and an invariant of the classical Euler equations of ideal (inviscid) fluid flow. The question addressed by Scheeler et al. is the extent to which the helicity remains invariant when fluid viscosity, unavoidable in reality, is taken into consideration.