Numerical insights into magnetic dynamo action in a turbulent regime

We report on hybrid numerical simulations of a turbulent magnetic dynamo. The simulated set-up mimics the Riga dynamo experiment characterized by Re ≈ 3.5 × 106 and (Gailitis et al 2000 Phys. Rev. Lett. 84 4365–8). The simulations were performed by a simultaneous fully coupled solution of the transient Reynolds-averaged Navier–Stokes (T-RANS) equations for the fluid velocity and turbulence field, and the direct numerical solution (DNS) of the magnetic induction equations. This fully integrated hybrid T-RANS/DNS approach, applied in the finite-volume numerical framework with a multi-block-structured nonorthogonal geometry-fitted computational mesh, reproduced the mechanism of self-generation of a magnetic field in close accordance with the experimental records. In addition to the numerical confirmation of the Riga findings, the numerical simulations provided detailed insights into the temporal and spatial dynamics of flow, turbulence and electromagnetic fields and their reorganization due to mutual interactions, revealing the full four-dimensional picture of a dynamo action in the turbulent regime under realistic working conditions.

[1]  R Volk,et al.  Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. , 2007, Physical review letters.

[2]  B. Dubrulle,et al.  Magnetic field reversals in an experimental turbulent dynamo , 2007, physics/0701076.

[3]  Osami Kitoh,et al.  Experimental study of turbulent swirling flow in a straight pipe , 1991, Journal of Fluid Mechanics.

[4]  Lathrop,et al.  Toward a self-generating magnetic dynamo: the role of turbulence , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Emmanuel Dormy,et al.  An integro-differential formulation for magnetic induction in bounded domains: boundary element-finite volume method , 2004 .

[6]  J. Pinton,et al.  An experimental Bullard–von Kármán dynamo , 2006 .

[7]  Suad Jakirlić,et al.  Modeling Rotating and Swirling Turbulent Flows: A Perpetual Challenge , 2002 .

[8]  G. Gerbeth,et al.  Colloquium: Laboratory experiments on hydromagnetic dynamos , 2002 .

[9]  Simulation and Identification of Deterministic Structures in Thermal and Magnetic Convection , 2002, Annals of the New York Academy of Sciences.

[10]  R. Stieglitz,et al.  The Karlsruhe Dynamo Experiment , 1999 .

[11]  Eddy-current-based momentum transfer method to suppress three-dimensional separation , 2005 .

[12]  Jean-François Pinton,et al.  Simulation of induction at low magnetic Prandtl number. , 2004, Physical review letters.

[13]  Gary A. Glatzmaier,et al.  Geodynamo Simulations—How Realistic Are They? , 2002 .

[14]  Jean-Paul Masson,et al.  Experimental study of super-rotation in a magnetostrophic spherical Couette flow , 2005, physics/0512217.

[15]  Dieter Biskamp,et al.  Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence , 2000 .

[16]  K. Hanjalic,et al.  A direct-numerical-simulation-based second-moment closure for turbulent magnetohydrodynamic flows , 2004 .

[17]  M. Rieutord,et al.  Magnetic structures in a dynamo simulation , 1996, Journal of Fluid Mechanics.

[18]  T. Gatski,et al.  Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach , 1991, Journal of Fluid Mechanics.

[19]  G. Gerbeth,et al.  The Riga Dynamo Experiment , 2003 .

[20]  F. Hamba.  Turbulent dynamo effect and cross helicity in magnetohydrodynamic flows , 1992 .

[21]  Paul H. Roberts,et al.  Geodynamo theory and simulations , 2000 .

[22]  Robert F. Stein,et al.  Dynamo-generated Turbulence and Large-Scale Magnetic Fields in a Keplerian Shear Flow , 1995 .

[23]  Parviz Moin,et al.  Large-eddy simulation of conductive flows at low magnetic Reynolds number , 2004 .

[24]  Daniele Carati,et al.  Dynamic gradient-diffusion subgrid models for incompressible magnetohydrodynamic turbulence , 2002 .

[25]  R. Wielebinski,et al.  Magnetic fields in galaxies , 1993 .

[26]  Sasa Kenjeres,et al.  On the implementation of effects of Lorentz force in turbulence closure models , 2000 .

[27]  R. Stieglitz,et al.  A two-scale hydromagnetic dynamo experiment , 2004, Journal of Fluid Mechanics.

[28]  T Gundrum,et al.  Magnetic field saturation in the Riga dynamo experiment. , 2001, Physical review letters.

[29]  Y. Ponty,et al.  Numerical study of dynamo action at low magnetic Prandtl numbers. , 2004, Physical review letters.

[30]  H. K. Moffatt.  Magnetic Field Generation in Electrically Conducting Fluids , 1978 .

[31]  K. Hanjali,et al.  Numerical insight into flow structure in ultraturbulent thermal convection. , 2002 .

[32]  F. Hamba.  Reynolds-averaged turbulence model for magnetohydrodynamic dynamo in a rotating spherical shell , 2004 .

[33]  F. Obermeier,et al.  Modelling of unsteady electromagnetically driven recirculating melt flows , 2004 .

[34]  Y. Ponty,et al.  Dynamo Regimes with a Nonhelical Forcing , 2005 .

[35]  F. Hamba,et al.  A turbulent dynamo model for the reversed field pinches of plasma , 1988 .

[36]  H. K. Moffatt.  Stretch, twist and fold , 1989, Nature.

[37]  S Kenjeres,et al.  Numerical simulation of a turbulent magnetic dynamo. , 2007, Physical review letters.

[38]  O. Agullo,et al.  Large eddy simulation of decaying magnetohydrodynamic turbulence with dynamic subgrid-modeling , 2001 .

[39]  Woodrow L. Shew,et al.  Liquid sodium model of geophysical core convection , 2005 .

[40]  Gerbeth,et al.  Detection of a flow induced magnetic field eigenmode in the riga dynamo facility , 2000, Physical review letters.

[41]  Sasa Kenjeres,et al.  LES, T-RANS and hybrid simulations of thermal convection at high Ra numbers , 2006 .

[42]  R. Stieglitz,et al.  Experiments at a two-scale dynamo test facility , 2006, Journal of Fluid Mechanics.

[43]  R. Stieglitz,et al.  Experimental demonstration of a homogeneous two-scale dynamo , 2000 .

[44]  M. Matsushima.  A scale-similarity model for the subgrid-scale flux with application to MHD turbulence in the Earth’s core , 2005 .

[45]  Reorganization of turbulence structure in magnetic Rayleigh-Benard convection: a T-RANS study , 2000 .

[46]  Paul H. Roberts,et al.  A three-dimensional self-consistent computer simulation of a geomagnetic field reversal , 1995, Nature.

[47]  S. Pope.  Ten questions concerning the large-eddy simulation of turbulent flows , 2004 .

[48]  K. Hanjalić,et al.  Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment , 2006 .

[49]  Sasa Kenjeres,et al.  Transient analysis of Rayleigh–Bénard convection with a RANS model , 1999 .

[50]  F. Plunian,et al.  Influence of electromagnetic boundary conditions onto the onset of dynamo action in laboratory experiments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  吉澤 徴,et al.  Hydrodynamic and magnetohydrodynamic turbulent flows : modelling and statistical theory , 1998 .

[52]  A. Yoshizawa.  Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields , 1990 .

[53]  B. Buffett.  A comparison of subgrid‐scale models for large‐eddy simulations of convection in the Earth's core , 2003 .

[54]  Akira Yoshizawa,et al.  Hydrodynamic and Magnetohydrodynamic Turbulent Flows , 1998 .

[55]  K. Hanjalic,et al.  RANS-Based Very Large Eddy Simulation of Thermal and Magnetic Convection at Extreme Conditions , 2006 .

[56]  Frank Stefani,et al.  Riga dynamo experiment and its theoretical background , 2004 .

[57]  Bassam A. Younis,et al.  Analysis and modelling of turbulent flow in an axially rotating pipe , 2000, Journal of Fluid Mechanics.

[58]  M. Christen,et al.  Dynamo experiments at the Riga sodium facility , 2002 .

[59]  Subgrid-scale modeling of compressible magnetohydrodynamic turbulence in heat-conducting plasma , 2006 .

[60]  F. Busse.  Homogeneous Dynamos in Planetary Cores and in the Laboratory , 2000 .