Numerical solutions of the three-dimensional magnetohydrodynamic alpha-model

Abstract

We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha-model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha-model correctly reproduce the growth rate of magnetic energy during the kinematic regime, but it also captures the nonlinear saturation level and the late generation of a large scale magnetic field by the helical turbulence.

12 pages, 19 figures

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Cited by in corpus (22)

• Shell to shell energy transfer in MHD, Part I: steady state turbulence
• Shell to shell energy transfer in MHD, Part II: Kinematic dynamo
• Analytical Study of Certain Magnetohydrodynamic-alpha Models
• Scale interactions in magnetohydrodynamic turbulence
• Analysis of a General Family of Regularized Navier-Stokes and MHD Models
• Dynamos at extreme magnetic Prandtl numbers: Insights from shell models
• Why dynamos are prone to reversals
• Inverse cascades and alpha-effect at low magnetic Prandtl number
• Magnetohydrodynamic activity inside a sphere
• Low magnetic Prandtl number dynamos with helical forcing
• Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling
• Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D
• Turbulent magnetic dynamo excitation at low magnetic Prandtl number
• A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets
• Wave turbulence in shallow water models
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
• The effect of subfilter-scale physics on regularization models
• High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model
• Self-truncation and scaling in Euler-Voigt-$\alpha$ and related fluid models
• Dynamo transition in a five-mode helical model
• The role of field correlations on turbulent dissipation