Normal and anomalous scaling in a problem of a passively advected magnetic field

Recently M. Vergassola [Phys. Rev. E 53, R3021 (1996)] considered the possibility of anomalous scaling in the three-dimensional dynamo problem. It has been shown that the two-point correlation function of magnetic field, advected by a white-in-time random velocity field with zero helicity has anomalous inertial-range scaling exponent in a statistically steady state. In this work we demonstrate that for the same problem the scaling of covariance of magnetic helicity is normal. The difference in scalings comes from the fact that unlike magnetic energy magnetic helicity in this problem is conserved. It is also conjectured that even small violation of parity invariance of the velocity field makes existence of the steady-state solution impossible.