On the existence of shear-current effects in magnetized burgulence

The possibility of explaining shear flow dynamos in terms of a magnetic shear-current effect (SC) is examined. A competing explanation is the incoherent $\alpha$-shear dynamo effect. Our primary diagnostics is the turbulent magnetic diffusivity tensor, in particular the off-diagonal diffusivity tensor component $\eta_{yx}$, a systematically negative sign of which would imply coherent dynamo action through SC. To be able to measure turbulent transport coefficients from systems with strong magnetic fluctuations, we present an extension of the test-field method that is capable of such measurements in the case where the pressure gradient term is dropped from the MHD equations, which is a nonlinear TFM (NLTFM). The hydrodynamic equation is related to Burger's equation and the resulting flows are referred to as magnetized burgulence. We use both kinetic and magnetic forcings, to mimic cases without and with simultaneous small-scale dynamo action. When the simplified MHD flow is forced kinetically, negative $\eta_{yx}$ values are obtained with exponential growth in both the radial and azimuthal magnetic field components. Using stochastic monochromatic magnetic forcing, the exponential growth is no longer seen, and NLTFM yields positive values of $\eta_{yx}$. In an attempt to recover the exponential growth seen in the kinetically forced case, we also employ an alternative forcing function with lowest $k$ vectors being removed - in this case the exponential growth is recovered, but the NLTFM results do not change dramatically. Our analysis of the dynamo numbers for the coherent SC and incoherent $\alpha$ and SC effects show that the incoherent effects are the main drivers of the dynamo instability in majority of cases. The coherent SC effect is mildly enhancing the dynamo action in the kinetically forced cases, while we find no evidence for magnetic SC in our simulations.