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ABSTRACT The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient β21 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 $$\mathcal {O}(10)$$ 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 urms ≃ brms, resulting in a positive total β21 even though $$\beta ^b_{21}\lt 0$$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation versus the spectral-τ closure, for which opposite signs for $$\beta ^u_{21}$$ have been reported, with the same sign for $$\beta ^b_{21}\lt 0$$. The results also offer an explanation for the simulations that find $$\beta ^u_{21}\gt 0$$ and an inconclusive overall sign of β21 for $$\mathcal {O}(10)$$ 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. 

ABSTRACT Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here, we introduce an error propagation formula that relaxes both limitations, allowing for non-linear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum – the latter being a non-linear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory.