Dynamo efficiency with shear in helical turbulence

To elucidate the influence of shear flow on the generation of magnetic field (the dynamo effect), we study the kinematic limit where the magnetic field does not backreact on the velocity field. By non-perturbatively incorporating the effect of shear in a helically forced turbulence, we show that turbulence intensity and turbulent transport coefficients (turbulent viscosity, $\alpha$ and $\beta$ effect) are enhanced by a weak shear while strongly suppressed for strong shear. In particular, $\beta$ is shown to be much more strongly suppressed than $\alpha$ effect. We discuss its important implications for dynamo efficiency, i.e. on the scaling of the dynamo number with differential rotation.