Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball
- 作者: Kazantsev S.1, Kardakov V.2
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隶属关系:
- Sobolev Institute of Mathematics
- Novosibirsk State University of Architecture and Civil Engineering
- 期: 卷 13, 编号 3 (2019)
- 页面: 480-499
- 栏目: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213224
- DOI: https://doi.org/10.1134/S1990478919030098
- ID: 213224
如何引用文章
详细
Under study is the polynomial orthogonal basis system of vector fields in the ball which corresponds to the Helmholtz decomposition and is divided into the three parts: potential, harmonic, and solenoidal. It is shown that the decomposition of a solenoidal vector field with respect to this basis is a poloidal-toroidal decomposition (the Mie representation). In this case, the toroidal potentials are Zernike polynomials, whereas the poloidal potentials are generalized Zernike polynomials. The polynomial system of toroidal and poloidal vector fields in a ball can be used for solving practical problems, in particular, to represent the geomagnetic field in the Earth’s core.
作者简介
S. Kazantsev
Sobolev Institute of Mathematics
编辑信件的主要联系方式.
Email: kazan@math.nsc.ru
俄罗斯联邦, pr. Akad. Koptyuga 4, Novosibirsk, 630090
V. Kardakov
Novosibirsk State University of Architecture and Civil Engineering
Email: kazan@math.nsc.ru
俄罗斯联邦, ul. Leningradskaya 113, Novosibirsk, 630113