Shear Alfvén waves in turbulent plasmas

The rate of decay of shear Alfvén waves along a magnetic field line of a diffusive plasma grows with the number of nodes of the initial perturbation. It is reasonable to think that the energy dissipation produced by this decay will be small if the perturbation was localized in a small set. This does not happen in turbulent plasmas: transport of the oscillation by the flow involves the whole domain. A general relation is obtained proving that the global energy dissipation is bounded below by an exponential of the number of nodes of any shear Alfvén wave along a segment of any field line of the average magnetic field.