On the shear-current effect: toward understanding why theories and simulations have mutually and separately conflicted

Abstract

The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient ${\beta }_{21}$ with a favorable negative sign for exponential mean-field growth, rather than positive for diffusion. There have been long standing disagreements among theoretical calculations and comparisons of theory with numerical experiments as to the sign of kinetic (${\beta }_{21}^u$) and magnetic (${\beta }_{21}^b$) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike ${\beta }_{21}^b$, the kinetic SCE ${\beta }_{21}^u$ has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at $\mathcal{O}(10)$ Reynolds numbers if the spectrum is not too steep. Conversely, ${\beta }_{21}^b$ is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive ${\beta }_{21}^u$ can dominate even at energy equipartition $u_{\text{rms}}\simeq b_{\text{rms}}$, resulting in a positive total ${\beta }_{21}$ even though ${\beta }_{21}^b<0$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation (SOCA) versus the spectral-$\tau$ closure (STC), for which opposite signs for ${\beta }_{21}^u$ have been reported, with the same sign for ${\beta }_{21}^b<0$. The results also offer an explanation for the simulations that find ${\beta }_{21}^u>0$ and an inconclusive overall sign of ${\beta }_{21}$ for $\mathcal{O}(10)$ Reynolds numbers. The transient behavior of ${\beta }_{21}^u$ is demonstrated using the kinematic test-field method. We compute dynamo growth rates for cases with or without rotation, and discuss opportunities for further work.

arXiv comment17 pages, 12 figures; accepted by MNRAS

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