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

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 favourable 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(u)(21)) and magnetic (beta(b)(21)) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike beta(b)(21), the kinetic SCE beta(u)(21) has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at O(10) Reynolds numbers if the spectrum is not too steep. Conversely, beta(b)(21) is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive beta(u)(21) can dominate even at energy equipartition u(rms) similar or equal to b(rms), resulting in a positive total beta(21) even though beta(b)(21) < 0. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation versus the spectral-tau closure, for which opposite signs for beta(u)(21) have been reported, with the same sign for beta(b)(21) < 0. The results also offer an explanation for the simulations that find beta(u)(21) > 0 and an inconclusive overall sign of beta(21) for O(10) Reynolds numbers. The transient behaviour of beta(u)(21) 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.

Automated summary

The study combines analytical approaches with simulations to investigate the shear-current effect in mean-field dynamo theory. The results show that the kinetic contribution can transition from positive to negative values with the kinetic energy spectral index, while the magnetic contribution remains negative regardless of the spectral index.