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• W2091516004 abstract "This special section of Fluid Dynamics Research includes five articles on vortex rings in both classical and quantum fluids. The leading scientists of the field describe the trends in and the state-of-the-art development of experiments, theories and numerical simulations of vortex rings. The year 2008 was the 150th anniversary of 'vortex motion' since Hermann von Helmholtz opened up this field. In 1858, Helmholtz published a paper in Crelle's Journal which put forward the concept of 'vorticity' and made the first analysis of vortex motion. Fluid mechanics before that was limited to irrotational motion. In the absence of vorticity, the motion of an incompressible homogeneous fluid is virtually equivalent to a rigid-body motion in the sense that the fluid motion is determined once the boundary configuration is specified. Helmholtz proved, among other things, that, without viscosity, a vortex line is frozen into the fluid. This Helmholtz's law immediately implies the preservation of knots and links of vortex lines and its implication is enormous. One of the major trends of fluid mechanics since the latter half of the 20th century is to clarify the topological meaning of Helmholtz's law and to exploit it to develop theoretical and numerical methods to find the solutions of the Euler equations and to develop experimental techniques to gain an insight into fluid motion. Vortex rings are prominent coherent structures in a variety of fluid motions from the microscopic scale, through human and mesoscale to astrophysical scales, and have attracted people's interest. The late professor Philip G Saffman (1981) emphasized the significance of studies on vortex rings. One particular motion exemplifies the whole range of problems of vortex motion and is also a commonly known phenomenon, namely the vortex ring or smoke ring. Vortex rings are easily produced by dropping drops of one liquid into another, or by puffing fluid out of a hole, or by exhaling smoke if one has the skill. Their formation is a problem of vortex sheet dynamics, the steady state is a problem of existence, their duration is a problem of stability, and if there are several we have the problem of vortex interactions. Helmholtz himself, in the same paper (1858), devoted a few pages to an analysis of the motion of a vortex ring, and made substantial contributions. Since then, theoretical, experimental and numerical treatments of vortex rings have been developing continuously, yet we encounter mysteries and novel phenomena, with which vortex rings find new applications in, say, bio-fluid mechanics. Recently vortex rings have enlarged their scope beyond classical fluids to encompass super-fluids and Bose–Einstein condensates. On the occasion of the 150th anniversary of Helmholtz's theory on a vortex ring, it is worthwhile to bring together, in one issue, the latest understandings of and open problems in vortex rings from various aspects. The topics in this issue include development of theories and experiments for motion of vortex rings and their interaction with other vortex rings, flows and boundaries, with application to vortex-ring manipulation for flow control, original experiments on collision of vortex rings with a porous boundary, a novel numerical technique to simulate three-dimensional motion of vortex rings and new theories of dynamics of quantum vortex rings governed by nonlinear Schrodinger equations. I hope that this special section gives a sketch, in some proportion, of the current frontier of the field and provides a means to tackle future problems. References Saffman P G 1981 Dynamics of vorticity J. Fluid Mech. 106 49–58 von Helmholtz H 1858 Uber Integrale der hydrodynamischen Gleichungen welche den Wirbelbewegungen entsprechen J. Reine Angew. Math. 55 25–55 (Engl. transl.: Tait P G 1867 On the integrals of the hydrodynamical equations which express vortex-motion Phil. Mag. 33 (4) 485–512)" @default.
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• W2091516004 date "2009-09-02" @default.
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• W2091516004 title "Special section on vortex rings" @default.
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• W2091516004 doi "https://doi.org/10.1088/1873-7005/41/5/051001" @default.
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