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

TL;DR

This paper numerically investigates the shear dynamo effect in turbulent flows across various regimes, demonstrating large-scale magnetic field growth even at low fluid Reynolds numbers, and compares results with analytical predictions.

Contribution

It explores dynamo action in previously unexamined parameter regimes, especially low Re, and computes turbulent transport coefficients using the test-field method.

Findings

Large-scale dynamo action occurs at Re < 1 with Rm > 1.

Growth rate scales linearly with shear.

Results agree with earlier analytical models.

Abstract

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.