Abstract
We present direct numerical simulations of decaying magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number. The domain considered is bounded by periodic boundary conditions in the two directions perpendicular to the magnetic field and by two plane Hartmann walls in the third direction. Regimes of high magnetic fields (Hartmann number of up to 896) are reached thanks to a new spectral method using the eigenvectors of the dissipation operator. The decay is found to proceed through two phases: first, energy and integral length scales vary rapidly during a twodimensionalisation phase extending over approximately a Hartmann friction time. During this phase, the evolution of the former appears significantly more impeded by the presence of walls than that of the latter. Once the large scales are nearly quasitwodimensional, the decay results from the competition of a twodimensional dynamics driven by dissipation in the Hartmann boundary layers and the threedimensional dynamics of smaller scales. In the later stages of the decay, threedimensionality subsists under the form of barrelshaped structures. A purely quasitwo dimensional decay entirely dominated by friction in the Hartmann layers is not reached because of residual dissipation in the bulk. However, this dissipation is not generated by the threedimensionality that subsists, but by residual viscous friction due to horizontal velocity gradients. In the process, the energy in the velocity component aligned with the magnetic field is found to be strongly suppressed, as is skewness. This result reproduces the experimental findings of Kolesnikov & Tsinober (Fluid Dyn., vol. 9, 1974, pp. 621–624), where, as in the present simulations, Hartmann walls were present.
Original language  English 

Pages (fromto)  605636 
Number of pages  12 
Journal  Journal of Fluid Mechanics 
Volume  783 
Early online date  26 Oct 2015 
DOIs  
Publication status  Published  25 Nov 2015 
Keywords
 highHartmannnumber flows
 MHD turbulence
 turbulence simulation
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Alban Potherat
 Research Centre for Fluid and Complex Systems  Centre Director
Person: Teaching and Research