F Plunian and R Stepanov 2007 New J. Phys. 9 294 doi:10.1088/1367-2630/9/8/294
A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence
Focus on Magnetohydrodynamics and the Dynamo ProblemF Plunian1,2,4 and R Stepanov3
Show affiliationsPart of Focus on Magnetohydrodynamics and the Dynamo Problem
We derive a new shell model of magnetohydrodynamic (MHD) turbulence in which the energy transfers are not necessarily local. Like the original MHD equations, the model conserves the total energy, magnetic helicity, cross-helicity and volume in phase space (Liouville's theorem) apart from the effects of external forcing, viscous dissipation and magnetic diffusion. The model of hydrodynamic (HD) turbulence is derived from the MHD model setting the magnetic field to zero. In that case the conserved quantities are the kinetic energy and the kinetic helicity. In addition to a statistically stationary state with a Kolmogorov spectrum, the HD model exhibits multiscaling. The anomalous scaling exponents are found to depend on a free parameter α that measures the non-locality degree of the model. In freely decaying turbulence, the infra-red spectrum also depends on α. Comparison with theory suggests using α = −5/2. In MHD turbulence, we investigate the fully developed turbulent dynamo for a wide range of magnetic Prandtl numbers in both kinematic and dynamic cases. Both local and non-local energy transfers are clearly identified.
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Issue 8 (August 2007)
Received 15 December 2006
Published 31 August 2007
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A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence
F Plunian and R Stepanov 2007 New J. Phys. 9 294
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