Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball
- Авторлар: Kazantsev S.1, Kardakov V.2
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Мекемелер:
- Sobolev Institute of Mathematics
- Novosibirsk State University of Architecture and Civil Engineering
- Шығарылым: Том 13, № 3 (2019)
- Беттер: 480-499
- Бөлім: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213224
- DOI: https://doi.org/10.1134/S1990478919030098
- ID: 213224
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
S. Kazantsev
Sobolev Institute of Mathematics
Хат алмасуға жауапты Автор.
Email: kazan@math.nsc.ru
Ресей, pr. Akad. Koptyuga 4, Novosibirsk, 630090
V. Kardakov
Novosibirsk State University of Architecture and Civil Engineering
Email: kazan@math.nsc.ru
Ресей, ul. Leningradskaya 113, Novosibirsk, 630113