Facilitating dynamo action via control of large-scale turbulence

A. Limone, D. R. Hatch, C. B. Forest, F. Jenko
2012 Physical Review E  
The magnetohydrodynamic dynamo effect is considered to be the major cause of magnetic field generation in geo-and astrophysical systems. Recent experimental and numerical results show that turbulence constitutes an obstacle to dynamos; yet its role in this context is not totally clear. Via numerical simulations, we identify large-scale turbulent vortices with a detrimental effect on the amplification of the magnetic field in a geometry of experimental interest, and propose a strategy for
more » ... ating the dynamo instability by manipulating these detrimental "hidden" dynamics. PACS numbers: 47.35.Tv, 07.55.Db, 95.30.Lz Introduction.-The magnetohydrodynamic (MHD) dynamo effect is considered to be the main cause of the generation of self-sustained magnetic fields in geo-and astrophysical objects [1]: The kinetic energy of an electrically conducting fluid can be transformed into magnetic energy, E M , as found analytically, experimentally, and numerically [2, 3, 5, 6]. A magnetic field B can be generated in a conducting fluid (e.g., liquid metal or plasma) when the advection term in the governing induction equation sufficiently dominates the diffusion term in order to amplify initial magnetic perturbations, and when the geometry of the flow is such that an amplification mechanism can occur. Recent experimental, analytical and numerical investigations [4, [7] [8] [9] [10] suggest that large-scale fluctuations of the flow constitute an obstacle to dynamos, which are sometimes not observed experimentally at Reynolds numbers where they are theoretically expected [11] . Strategies are needed in order to overcome this problem, and turbulence control is considered to be the key action to take [10]. We study numerically dynamo action in a turbulent flow that is stirred by a large-scale, constant axisymmetric force in spherical geometry, as in the Madison Dynamo Experiment (MDE) [11] . The force creates a two-vortex flow around the z axis (the so-called s2t2 flow), previously studied numerically by Dudley and James [15] who suggested it as a flow which optimizes the magnetic field generation. We carried out simulations using the DYNAMO code [16, 17] , a pseudo-spectral code which mimics the conditions of the MDE, in order to identify the vortices with possible negative effects, characterized their scale and their temporal evolution, and finally proposed practical strategies whereby these vortices may be controlled experimentally. In order to understand which configurations are detrimental for the dynamo process, we analyze the simulated velocity fields via Singular Value Decomposition (SVD), a mathematical method used in order to simplify the representation of datasets (see [18] or [19] for its applications to fluid dynamics). SVD reduces the number of variables necessary to quantify the properties of the data under analysis: One can limit oneself to analyzing only the information described typically by the first few new variables. A generic spatio-temporal field
doi:10.1103/physreve.86.066315 pmid:23368046 fatcat:ewzanogqgfe3rogxip5fameoty