Computational MHD Part II — Application to a Nonlinear Dynamo Model

  • Egbert Zienicke
  • Hélène Politano
  • Annick Pouquet
Part of the International Centre for Mechanical Sciences book series (CISM, volume 418)


Lagrangian chaos of the underlying flow is the driving force for the fast dynamo based on the strectch-twist-fold mechanism on small scales. In this contribution the hypothesis that the magnetic field by the action of the Lorentz force supresses Lagrangian chaos is checked by direct numerical simulations of the MHD equations. As a measure of the level of chaos the Lyapunov exponent of a set of 128 × 128 trajectories of fluid particles is computed in the growth phase and in the saturated phase of the dynamo when the magnetic field has reached its final strength. The numerical code, based on a pseudospectral algorithm, is developped for parallel computation on a multiprocessor system. Magnetic Reynolds numbers up to 240 and scale separations between the wavelength of the hydrodynamical forcing and the scale of the computational domain up to four are reached. For the runs were the kinetic Reyold number is high enough that the hydrodynamical bifurcation sequence to a more chaotic flow already has taken place, the mean value of the Lyapunov exponent is noticeable diminished in the saturated phase compared to the growth phase of the dynamo.


Lyapunov Exponent Direct Numerical Simulation Magnetic Helicity Scale Separation Saturated Phase 
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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Egbert Zienicke
    • 1
  • Hélène Politano
    • 2
  • Annick Pouquet
    • 2
  1. 1.Fakultät MaschinenbauUniversität IlmenauGermany
  2. 2.Observatoire de la Côte d’AzurNiceFrance

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