Numerical studies of dynamo action in a turbulent shear flow. I.

Abstract

We perform numerical experiments to study the shear dynamo problem where we look for the growth of a large-scale magnetic field due to non-helical stirring at small scales in a background linear shear flow in previously unexplored parameter regimes. We demonstrate the large-scale dynamo action in the limit where the fluid Reynolds number ($\operatorname{Re}$) is below unity while the magnetic Reynolds number (${\rm Rm}$) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low $\operatorname{Re}$ is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus attention on this analytically more tractable limit of $\operatorname{Re}\lt 1$ compared to the more formidable limit of $\operatorname{Re}\gt 1$. We also perform simulations in the regimes where (i) both ($\operatorname{Re}$, ${\rm Rm}$) < 1, and (ii) $\operatorname{Re}\gt 1$ and ${\rm Rm}\lt 1$, and compute all of the components of the turbulent transport coefficients (${{\alpha }_{ij}}$ and ${{\eta }_{ij}}$) using the test-field method. A reasonably good agreement is observed between our results and the results of earlier analytical works in similar parameter regimes.