Shear-current effect in a turbulent convection with a large-scale shear

The shear-current effect in a nonrotating homogeneous turbulent convection with a large-scale constant shear is studied. The large-scale velocity shear causes anisotropy of turbulent convection, which produces the mean electromotive force $\text{bec}{\mathcal{E}}^{(W)}\propto \mathbf{W}\times \mathbf{J}$ and the mean electric current along the original mean magnetic field, where $\mathbf{W}$ is the background mean vorticity due to the shear and $\mathbf{J}$ is the mean electric current. This results in a large-scale dynamo even in a nonrotating and nonhelical homogeneous sheared turbulent convection, whereby the $\alpha$ effect vanishes. It is found that turbulent convection promotes the shear-current dynamo instability, i.e., the heat flux causes positive contribution to the shear-current effect. However, there is no dynamo action due to the shear-current effect for small hydrodynamic and magnetic Reynolds numbers even in a turbulent convection, if the spatial scaling for the turbulent correlation time is $\tau (k)\propto k^{-2}$, where $k$ is the small-scale wave number.