Advertisement

Asymptotic structure of fast dynamo eigenfunctions

  • B. J. Bayly
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)

Abstract

The eigenfunctions of the kinematic dynamo problem exhibit complicated spatial structure when the magnetic diffusivity is small. When the base flow is spatially periodic, we may study this structure by examining the Fourier components of the eigenfunction at large wavevectors. In this regime we may seek a WKB form in terms of slowly-varying functions of wavevector. The resulting hierarchy of equations may be systematically analysed for both zero and small nonzero diffusivities.

Keywords

Eikonal Equation Induction Equation Magnetic Diffusivity Dynamo Action Asymptotic Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnold, V. I. & Korkina, E. I. 1983 The growth of a magnetic field in a three-dimensional steady incompressible flow. Vest. Mask. Un. Ta. Ser. 1, Matem. Mekh. no. 3, 43–46.Google Scholar
  2. Bayly, B. J. 1993 Scalar dynamo models. Geo. Astro. Fluid Dyn.73, 61–74.MathSciNetCrossRefADSGoogle Scholar
  3. Childress, S. & Gilbert, A. D. 1995 Stretch, Twist, Fold: The Fast Dynamo, Springer.Google Scholar
  4. Du, Y., Tel, T., & Ott, E. 1994 Characterization of sign-singular measures. Physica D76, 168–180.CrossRefMathSciNetADSzbMATHGoogle Scholar
  5. Galloway, D. J. & Frisch, U. 1986 Dynamo action in a family of flows with chaotic streamlines. Geo. Astro. Fluid Dyn.36, 53–83.MathSciNetADSCrossRefGoogle Scholar
  6. Lau, Y.-T. & Finn, J. M. 1993 Fast dynamos with finite resistivity in steady flows with stagnation points. Phys. Fluids B5, 365–375.MathSciNetADSCrossRefGoogle Scholar
  7. Moffatt, H. K. & Proctor, M. R. E. 1985 Topological constraints associated with fast dynamo action. J. Fluid Mech.154, 493–507.ADSzbMATHCrossRefGoogle Scholar
  8. Vainshtein, S. I. & Zeldovich, YA. B. 1972 Origin of magnetic fields in astrophysics. Usp. Fiz. Nauk106, 431–457. [English translation: Sov. Phys. Usp. 15, 159–172.]ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • B. J. Bayly
    • 1
  1. 1.Mathematics Dept.University of ArizonaTucsonUSA

Personalised recommendations