| Summary: | Idealized fluids possess a topological conserved quantity: helicity, which measures the average linking of vortex field-lines. Despite its relevance across a range of flows, the fact that helicity has never been measured in a real fluid renders this conserved quantity and its dynamics in the presence of viscosity poorly understood. Enabled by a collection of novel experimental techniques and theoretical frameworks, here we report the first measurements of fluid helicity in classical flows composed of thin-core vortex tubes. Our measurements show that viscous flows can conserve helicity---both during smooth deformations of the field as well as through discontinuous, topology changing reconnection events---by efficiently transferring helicity between forms. In addition to demonstrating helicity conservation in both inviscid and viscously dominated regimes, these results provide an understanding of how the geometrically distinct components of helicity are dynamically related, while illustrating the unique role that each plays during the evolution of a vortex. These results open the door to quantitative investigation of the constraints that vortex field-line geometry imposes on real flows, and provide a lens for approaching previously complex problems in fluids, ranging from turbulent flows to plasmas.
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