Applied Mathematics and Mechanics

, Volume 18, Issue 10, pp 997–1002 | Cite as

On force-free magnetic fields and beltrami flows

  • Feng Qingzeng


Solenoidal vector fields, which satisfy the condition that the field vector everywhere parallels to its curl, have complex topological structures, and usually show chaotic behaviors. In this paper, analytical solutions for vector fields with constant proportional factor in three basic coordinate systems are presented and it is pointed out that a Beltrami flow can sustain a steady force-free magnetic field in a perfectly conducting fluid, provided the magnetic field is parallel to the velocity everywhere.

Key words

analytical solutions maximal helicity chaotic lines of force 


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  1. [1]
    R. Lüst and S. Schlüter, Kraftfreie magnetfelder, Z. Astrophys., 34 (1954), 263–282.Google Scholar
  2. [2]
    L. Woltjer, A theorem on force-free magnetic fields, Proc. Nat. Acad. Sci. USA, 44 (1958), 489–491.Google Scholar
  3. [3]
    H. K. Moffatt, The degree of knottedness of tangled vortex lines, J. Fluid Mech., 35 (1969), 117–129.Google Scholar
  4. [4]
    V. I. Arnold, Sur la topologie des écoulements stationaires des fluides parfaits, C. R. Acad. Sci. Paris, 26 (1965), 17–20.Google Scholar
  5. [5]
    T. Dombre, et al., Chaotic streamlines and Lagrangian turbulences: the ABC flow, J. Fluid Mech., 16, 7 (1986), 353.Google Scholar
  6. [6]
    S. Chandrasekhar, On force-free magnetic fields, Proc. Nat. Acad. Sci. USA. 42 (1956), 1–5.Google Scholar
  7. [7]
    W. M. Elssasser, Introduction effects in terrestrial magnetism, Phys. Rev., 69 (1946), 106–116.Google Scholar
  8. [8]
    R. H. G. Helleman, Self-generated chaotic behavior in nonlinear mechanics, in Fundamental Problems in Statistical Mechanics, Vol. 5 eds. by E. D. G. Cohen, North-Holland (1980), 165–233.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Feng Qingzeng
    • 1
    • 2
  1. 1.National Laboratory for Turbulence ResearchPeking UniversityBeijingPeoples Republic of China
  2. 2.Department of Mechanics and Engineering SciencePeking UniversityBeijingPeoples Republic of China

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