Exact Beltrami flows in a spherical shell
- 31 August 2021
- journal article
- research article
- Published by Walter de Gruyter GmbH in Zeitschrift für Naturforschung A
- Vol. 76 (11), 1007-1018
- https://doi.org/10.1515/zna-2021-0236
Abstract
Exact flows of an incompressible fluid satisfying the Beltrami equation inside a spherical shell are constructed in the Cartesian coordinates in terms of elementary functions. Two scale-invariant equations defining two infinite series of eigenvalues λ n and λ̃m${\tilde {\lambda }}_{m}$ of the operator curl in the shell with the nonpenetration boundary conditions on the boundary spheres are derived. The corresponding eigenfields are presented in explicit form and their symmetries are investigated. Asymptotics of the eigenvalues λ n and λ̃m${\tilde {\lambda }}_{m}$ at n , m → ∞ are obtained.Keywords
This publication has 12 references indexed in Scilit:
- Vortex knots for the spheromak fluid flow and their moduli spacesJournal of Mathematical Analysis and Applications, 2017
- Eigenfunctions of the curl in cylindrical geometryJournal of Mathematical Physics, 2005
- The spectrum of the curl operator on spherically symmetric domainsPhysics of Plasmas, 2000
- Eigenfunctions of the curl operator in spherical coordinatesJournal of Mathematical Physics, 1994
- Discrete Eigenstates of Plasmas Described by the Chandrasekhar-Kendall FunctionsProgress of Theoretical Physics, 1991
- Remarks on spectra of operator rotMathematische Zeitschrift, 1990
- Exact solutions of the Navier-Stokes equations-the generalized Beltrami flows, review and extensionActa Mechanica, 1990
- MHD stability of SpheromakNuclear Fusion, 1979
- On Force-Free Magnetic Fields.The Astrophysical Journal, 1957
- ON FORCE-FREE MAGNETIC FIELDSProceedings of the National Academy of Sciences of the United States of America, 1956