Book chapter
Vortex Crystals
Advances in Applied Mechanics, pp 1-79
2003
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional (2D) flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of ‘special functions’ arising in classical mathematical physics have been revealed. Vortex motion on 2D manifolds such as the sphere, the cylinder (periodic strip) and the torus (periodic parallelogram) has also been studied because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.
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Details
- Title
- Vortex Crystals
- Creators
- Hassan Aref - University of Illinois Urbana-ChampaignPaul K. Newton - University of Southern CaliforniaMark A. Stremler - Vanderbilt UniversityTadashi Tokieda - Université de MontréalDmitri L. Vainchtein - University of California, Santa Barbara
- Publication Details
- Advances in Applied Mechanics, pp 1-79
- Publisher
- Elsevier Science & Technology
- Resource Type
- Book chapter
- Language
- English
- Academic Unit
- C. and J. Nyheim Plasma Institute
- Web of Science ID
- WOS:000186916200001
- Scopus ID
- 2-s2.0-0141651117
- Other Identifier
- 991021861867204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Engineering, Mechanical
- Mechanics