Dynamo Quenching Due to Shear Flow

We provide a theory of dynamo ($\alpha$ effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the $\alpha$ effect is reduced by the shear even in the absence of magnetic field. The $\alpha$ effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun.