{"title":"二维磁流体流中的奥布-魏斯型拓扑标准","authors":"B.K. Shivamoggi, G.J.F. van Heijst, L.P.J. Kamp","doi":"10.1017/s0022377824000436","DOIUrl":null,"url":null,"abstract":"<p>The Okubo–Weiss (Okubo, <span>Deep-Sea Res.</span>, vol. 17, issue 3, 1970, pp. 445–454; Weiss, <span>Physica D</span>, vol. 48, issue 2, 1991, pp. 273–294) criterion has been widely used as a diagnostic tool to divide a two-dimensional (2-D) hydrodynamical flow field into hyperbolic and elliptic regions. This paper considers extension of these ideas to 2-D magnetohydrodynamic (MHD) flows, and presents an Okubo–Weiss-type criterion to parameterize the magnetic field topology in 2-D MHD flows. This ensues via its topological connections with the intrinsic metric properties of the underlying magnetic flux manifold, and is illustrated by recasting the Okubo–Weiss-type criterion via the 2-D MHD stationary generalized Alfvénic state condition to approximate the slow-flow-variation ansatz imposed in its derivation. The Okubo–Weiss-type parameter then turns out to be related to the sign definiteness of the Gaussian curvature of the magnetic flux manifold. A similar formulation becomes possible for 2-D electron MHD flows, by using the generalized magnetic flux framework to incorporate the electron-inertia effects. Numerical simulations of quasi-stationary vortices in 2-D MHD flows in the decaying turbulence regime are then given to demonstrate that the Okubo–Weiss-type criterion is able to separate the MHD flow field into elliptic and hyperbolic field configurations very well.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"47 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Okubo–Weiss-type topological criteria in two-dimensional magnetohydrodynamic flows\",\"authors\":\"B.K. Shivamoggi, G.J.F. van Heijst, L.P.J. Kamp\",\"doi\":\"10.1017/s0022377824000436\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The Okubo–Weiss (Okubo, <span>Deep-Sea Res.</span>, vol. 17, issue 3, 1970, pp. 445–454; Weiss, <span>Physica D</span>, vol. 48, issue 2, 1991, pp. 273–294) criterion has been widely used as a diagnostic tool to divide a two-dimensional (2-D) hydrodynamical flow field into hyperbolic and elliptic regions. This paper considers extension of these ideas to 2-D magnetohydrodynamic (MHD) flows, and presents an Okubo–Weiss-type criterion to parameterize the magnetic field topology in 2-D MHD flows. This ensues via its topological connections with the intrinsic metric properties of the underlying magnetic flux manifold, and is illustrated by recasting the Okubo–Weiss-type criterion via the 2-D MHD stationary generalized Alfvénic state condition to approximate the slow-flow-variation ansatz imposed in its derivation. The Okubo–Weiss-type parameter then turns out to be related to the sign definiteness of the Gaussian curvature of the magnetic flux manifold. A similar formulation becomes possible for 2-D electron MHD flows, by using the generalized magnetic flux framework to incorporate the electron-inertia effects. Numerical simulations of quasi-stationary vortices in 2-D MHD flows in the decaying turbulence regime are then given to demonstrate that the Okubo–Weiss-type criterion is able to separate the MHD flow field into elliptic and hyperbolic field configurations very well.</p>\",\"PeriodicalId\":16846,\"journal\":{\"name\":\"Journal of Plasma Physics\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-04-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Plasma Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1017/s0022377824000436\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Plasma Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1017/s0022377824000436","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
The Okubo–Weiss-type topological criteria in two-dimensional magnetohydrodynamic flows
The Okubo–Weiss (Okubo, Deep-Sea Res., vol. 17, issue 3, 1970, pp. 445–454; Weiss, Physica D, vol. 48, issue 2, 1991, pp. 273–294) criterion has been widely used as a diagnostic tool to divide a two-dimensional (2-D) hydrodynamical flow field into hyperbolic and elliptic regions. This paper considers extension of these ideas to 2-D magnetohydrodynamic (MHD) flows, and presents an Okubo–Weiss-type criterion to parameterize the magnetic field topology in 2-D MHD flows. This ensues via its topological connections with the intrinsic metric properties of the underlying magnetic flux manifold, and is illustrated by recasting the Okubo–Weiss-type criterion via the 2-D MHD stationary generalized Alfvénic state condition to approximate the slow-flow-variation ansatz imposed in its derivation. The Okubo–Weiss-type parameter then turns out to be related to the sign definiteness of the Gaussian curvature of the magnetic flux manifold. A similar formulation becomes possible for 2-D electron MHD flows, by using the generalized magnetic flux framework to incorporate the electron-inertia effects. Numerical simulations of quasi-stationary vortices in 2-D MHD flows in the decaying turbulence regime are then given to demonstrate that the Okubo–Weiss-type criterion is able to separate the MHD flow field into elliptic and hyperbolic field configurations very well.
期刊介绍:
JPP aspires to be the intellectual home of those who think of plasma physics as a fundamental discipline. The journal focuses on publishing research on laboratory plasmas (including magnetically confined and inertial fusion plasmas), space physics and plasma astrophysics that takes advantage of the rapid ongoing progress in instrumentation and computing to advance fundamental understanding of multiscale plasma physics. The Journal welcomes submissions of analytical, numerical, observational and experimental work: both original research and tutorial- or review-style papers, as well as proposals for its Lecture Notes series.