{"title":"六边形贝尔特拉米流中结结或连接的漩涡管的晶体状排列","authors":"Takahiro Nishiyama","doi":"10.1007/s00162-025-00748-y","DOIUrl":null,"url":null,"abstract":"<div><p>When knotted or linked vortex tubes are considered in real-analytic steady Euler flows, the flows should be Beltrami flows with constant proportionality factors that have chaotic streamlines. In this study, four types of such Beltrami flows were derived on the assumption that the set of streamlines in each flow had hexagonal symmetry. Their systematic derivation was enabled by information provided via crystallography, which is applicable to spatially periodic objects not restricted to chemical materials. Invariant tori, which are stream and vortex tubes in Beltrami flows, were numerically investigated using various proportionality factors and initial points for the derived hexagonal flows. As a result, a variety of knotted or linked invariant tori were found to be arranged as atoms in hexagonal crystals. Some invariant tori were observed to form infinitely spreading chains with link structures similar to those of chain-mail-like polycatenanes in chemistry.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"39 4","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-025-00748-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Crystal-like arrangements of knotted or linked vortex tubes in hexagonal Beltrami flows\",\"authors\":\"Takahiro Nishiyama\",\"doi\":\"10.1007/s00162-025-00748-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>When knotted or linked vortex tubes are considered in real-analytic steady Euler flows, the flows should be Beltrami flows with constant proportionality factors that have chaotic streamlines. In this study, four types of such Beltrami flows were derived on the assumption that the set of streamlines in each flow had hexagonal symmetry. Their systematic derivation was enabled by information provided via crystallography, which is applicable to spatially periodic objects not restricted to chemical materials. Invariant tori, which are stream and vortex tubes in Beltrami flows, were numerically investigated using various proportionality factors and initial points for the derived hexagonal flows. As a result, a variety of knotted or linked invariant tori were found to be arranged as atoms in hexagonal crystals. Some invariant tori were observed to form infinitely spreading chains with link structures similar to those of chain-mail-like polycatenanes in chemistry.</p></div>\",\"PeriodicalId\":795,\"journal\":{\"name\":\"Theoretical and Computational Fluid Dynamics\",\"volume\":\"39 4\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00162-025-00748-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Computational Fluid Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00162-025-00748-y\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Computational Fluid Dynamics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00162-025-00748-y","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Crystal-like arrangements of knotted or linked vortex tubes in hexagonal Beltrami flows
When knotted or linked vortex tubes are considered in real-analytic steady Euler flows, the flows should be Beltrami flows with constant proportionality factors that have chaotic streamlines. In this study, four types of such Beltrami flows were derived on the assumption that the set of streamlines in each flow had hexagonal symmetry. Their systematic derivation was enabled by information provided via crystallography, which is applicable to spatially periodic objects not restricted to chemical materials. Invariant tori, which are stream and vortex tubes in Beltrami flows, were numerically investigated using various proportionality factors and initial points for the derived hexagonal flows. As a result, a variety of knotted or linked invariant tori were found to be arranged as atoms in hexagonal crystals. Some invariant tori were observed to form infinitely spreading chains with link structures similar to those of chain-mail-like polycatenanes in chemistry.
期刊介绍：
Theoretical and Computational Fluid Dynamics provides a forum for the cross fertilization of ideas, tools and techniques across all disciplines in which fluid flow plays a role. The focus is on aspects of fluid dynamics where theory and computation are used to provide insights and data upon which solid physical understanding is revealed. We seek research papers, invited review articles, brief communications, letters and comments addressing flow phenomena of relevance to aeronautical, geophysical, environmental, material, mechanical and life sciences. Papers of a purely algorithmic, experimental or engineering application nature, and papers without significant new physical insights, are outside the scope of this journal. For computational work, authors are responsible for ensuring that any artifacts of discretization and/or implementation are sufficiently controlled such that the numerical results unambiguously support the conclusions drawn. Where appropriate, and to the extent possible, such papers should either include or reference supporting documentation in the form of verification and validation studies.
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