An anisotropically forced passive vector model is analyzed at scales much smaller and larger than the forcing scale by solving exactly the equation for the pair correlation function. The model covers the cases of magnetohydrodynamic turbulence, the linear pressure model, and the linearized Navier-Stokes equations by choice of a simple parameter. We determine whether or not the anisotropic injection mechanism induces dominance of the anisotropic effects at the asymptotic scaling regimes. We also show that under very broad conditions, both scaling regimes exhibit anomalous scaling due to the existence of nontrivial zero modes.

• Received 2 December 2008

DOI:https://doi.org/10.1103/PhysRevE.79.056303