Schumann, U. (1976) Numerical simulation of the transition from three to twodimensional turbulence under a uniform magnetic field. Journal of Fluid Mechanics, 74, pp. 3158. DOI: 10.1017/S0022112076001675.

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Official URL: http://www.jfm.damtp.cam.ac.uk/
Abstract
The transition of homogeneous turbulence from an initially isotropic threedimensional to a quasitwodimensional state is simulated numerically for a conducting, incompressible fluid under a uniform magnetic field B<sub>0</sub>. The magnetic Reynolds number is assumed to be small, so that the induced fluctuations of the magnetic field are small compared with the imposed magnetic field B<sub>0</sub>, and can be computed from a quasistatic approximation. If the imposed magnetic field is strong enough, all variations of the flow field in the direction of B<sub>0</sub> are damped out. This effect is important e.g. in the design of liquidmetal cooling systems for fusion reactors, and the properties of the final state are relevant to atmospheric turbulence. An extended version of the code of Orszag and Patterson (1972) is used to integrate the NavierStokes equations for an incompressible fluid. The initial hydrodynamic Reynolds number is 60. The magnetic interaction number N is varied between zero and 50. Periodic boundary conditions are used. The resolution corresponds to 323 points in real space. The full nonlinear simulations are compared with otherwise identical linear simulations; the linear results agree with the nonlinear ones within 3% for about onefifth of the largescale turnover time. This departure is a consequence of the returntoequilibrium tendencies caused mainly by energy transfer towards high wavenumbers. The angular energy transfer and the energy exchange between different components are smaller, and become virtually zero for large values of N. For N [approximate] 50 we reach a quasitwodimensional state. Here, the energy transfer towards high wavenumbers is reduced for the velocity components perpendicular to B<sub>0</sub> but relatively increased for the component parallel to B<sub>0</sub>. The overall behaviour is more similar to threethan to purely twodimensional turbulence. This finding is of great importance for turbulence models of the atmosphere. The realization of a purely twodimensional state does not seem to be possible for decaying turbulence. The magnetic field causes highly intensified pressure fluctuations, which contribute to the redistribution of the anisotropic Lorentz forcing.
Document Type:  Article  

Title:  Numerical simulation of the transition from three to twodimensional turbulence under a uniform magnetic field  
Authors: 
 
Date:  1976  
Journal or Publication Title:  Journal of Fluid Mechanics  
Volume:  74  
DOI:  10.1017/S0022112076001675  
Page Range:  pp. 3158  
Status:  Published  
Keywords:  incompressible fluid, nonlinear simulations  
HGF  Research field:  other  
HGF  Program:  other  
HGF  Program Themes:  other  
DLR  Research area:  no assignement  
DLR  Program:  no assignment  
DLR  Research theme (Project):  other  
Location:  Oberpfaffenhofen  
Institutes and Institutions:  Institute of Atmospheric Physics  
Deposited By:  Jana Freund  
Deposited On:  18 Nov 2008  
Last Modified:  12 Dec 2013 20:30 
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