Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 7
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Normand, C. 2008. Modal versus energy stability analysis of kinematic dynamos in cylindrical configurations. Physics of Fluids, Vol. 20, Issue. 8, p. 084105.

    Zabielski, L. and Mestel, A. J. 2006. Nonlinear dynamos in laminar, helical pipe flow. Physics of Fluids, Vol. 18, Issue. 4, p. 043602.

    Essén, Hanno 2004. Magnetohydrodynamic self-consistent exact helical solutions. Journal of Physics A: Mathematical and General, Vol. 37, Issue. 41, p. 9831.

    Dobler, Wolfgang Frick, Peter and Stepanov, Rodion 2003. Screw dynamo in a time-dependent pipe flow. Physical Review E, Vol. 67, Issue. 5,

    Gilbert, Andrew D. 2003.

    Dobler, Wolfgang Shukurov, Anvar and Brandenburg, Axel 2002. Nonlinear states of the screw dynamo. Physical Review E, Vol. 65, Issue. 3,

    Gilbert, Andrew D. and Ponty, Yannick 2000. Dynamos on stream surfaces of a highly conducting fluid. Geophysical & Astrophysical Fluid Dynamics, Vol. 93, Issue. 1-2, p. 55.

  • Journal of Fluid Mechanics, Volume 343
  • July 1997, pp. 375-406

Nonlinear equilibration of a dynamo in a smooth helical flow

  • DOI:
  • Published online: 01 July 1997

We investigate the nonlinear equilibration of magnetic fields in a smooth helical flow at large Reynolds number Re and magnetic Reynolds number Rm with Re[Gt ]Rm[Gt ]1. We start with a smooth spiral Couette flow driven by boundary conditions. Such flows act as dynamos, that is are unstable to growing magnetic fields; here we disregard purely hydrodynamic instabilities such as Taylor–Couette modes. The dominant feedback from a magnetic field mode is only on the mean flow and this yields a simplified ‘mean-flow system’ consisting of one magnetic mode and the mean flow, which we solve numerically. We also obtain the asymptotic structure of the equilibrated fields for weakly and strongly nonlinear regimes. In particular the field tends to concentrate in a cylindrical shell where all stretching and differential rotation is suppressed by the Lorentz force, and the fluid is in solid-body motion. This shell is bounded by thin diffusive layers where the stretching that maintains the field against diffusive decay is dominant.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *