Anomalous scalings and dynamics of magnetic helicity

It is demonstrated that the two-point correlation function of the magnetic helicity in the case of zero mean magnetic held has anomalous scalings for both compressible and incompressible turbulent helical fluid flow. The magn etic helicity in the limit of very high electrical conductivity is conserve d. This implies that the two-point correlation function of the conserved pr operty does not necessarily have normal scaling. The reason for the anomalo us scalings of the magnetic helicity correlation function is that the magne tic field in the equation for the two-point correlation function of the mag netic helicity plays a role of a pumping with anomalous scalings. It is sho wn also that when magnetic fluctuations with zero mean magnetic field are g enerated the magnetic helicity is very small even if the hydrodynamic helic ity is large, [S1063-651X(99)09703-2].