We perform numerical experiments to study the shear dynamo problem where we look for the growth of 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 when the fluid Reynolds number (${ \rm Re}$) is below unity whereas 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 ${ \rm Re}$ is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus the attention to this analytically more tractable limit of ${ \rm Re} < 1$ as compared to more formidable limit of ${ \rm Re} > 1$. We also perform simulations in the regimes when, (i) both (${ \rm Re}$, ${ \rm Rm}$) $< 1$; (ii) ${ \rm Re} > 1$ & ${ \rm Rm} < 1$, and compute all components of the turbulent transport coefficients ($\alpha_{ ij}$ and $\eta_{ ij}$) using the test--field method. A reasonably good agreement is seen between our results and the results of earlier analytical works (Sridhar & Singh 2010; Singh & Sridhar 2011) in the similar parameter regimes.
Categories: astro-ph.GA physics.flu-dyn