Numerical solutions of the three-dimensional magnetohydrodynamic   alpha-model
  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. 
P.D. Mininni (NCAR), D.C. Montgomery (Dartmouth), A. Pouquet (NCAR)