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Creation and dynamics of knotted vortices

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Abstract

Knots and links have been conjectured to play a fundamental role in a wide range of physical fields, including plasmas and fluids, both quantum and classical. In fluids, the fundamental knottedness-carrying excitations occur in the form of linked and knotted vortex loops, which have been conjectured to exist for over a century. Although they have been the subject of considerable theoretical study, their creation in the laboratory has remained an outstanding experimental goal. Here we report the creation of isolated trefoil vortex knots and pairs of linked vortex rings in water using a new method of accelerating specially shaped hydrofoils. Using a high-speed scanning tomography apparatus, we measure their three-dimensional topological and geometrical evolution in detail. In both cases we observe that the linked vortices stretch themselves and then deform—as dictated by their geometrically determined energy—towards a series of local vortex reconnections. This work establishes the existence and dynamics of knotted vortices in real fluids.

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Figure 1: The creation of vortices with designed shape and topology.
Figure 2: Scaling of trefoil knot vortex loops.
Figure 3: Topological evolution of linked and knotted vortex loops in three dimensions.
Figure 4: Topological and energetic evolution of several types of vortex loop.
Figure 5: Reconstruction of the vortex core and flow field from raw 3D data.

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Acknowledgements

The authors acknowledge useful discussions with J. Burton, P. M. Chaikin, E. Efrati, H. M. Jaeger, H. K. Moffatt, S. R. Nagel, M. Scheeler, T. Witten and W. Zhang. We acknowledge MRSEC Shared Facilities at the University of Chicago (DMR-0820054) for the use of their instruments. This work was supported by the National Science Foundation (NSF) Materials Research and Engineering Centers (MRSEC) Program at the University of Chicago (DMR-0820054). W.T.M.I. further acknowledges support from the A.P. Sloan Foundation through a Sloan fellowship, and the Packard Foundation through a Packard fellowship.

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Contributions

W.T.M.I. conceived and supervised research. W.T.M.I. and D.K. designed experiments and developed vortex generation and analysis techniques. D.K. developed the tomography apparatus and software, performed experiments and processed data. D.K. and W.T.M.I. analysed results and wrote the manuscript.

Corresponding authors

Correspondence to Dustin Kleckner or William T. M. Irvine.

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The authors declare no competing financial interests.

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Kleckner, D., Irvine, W. Creation and dynamics of knotted vortices. Nature Phys 9, 253–258 (2013). https://doi.org/10.1038/nphys2560

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