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tokens: the discrepancy is that the numerical values are obtained by fitting where V (1) and H (1) are considered independent. The second major difference is that the numerical data for sufficiently rapid rotation (Ω ⋆ ≳ 1) is incompatible with expressions of V and H which consider only terms proportional to sin 2 θ . Furthermore, in the foregoing analysis the anisotropy parameter a was kept as a free parameter and tuned such that in the slow rotation limit. It is also possible to compute a directly using Eq. (A14) in Appendix A of Kitchatinov Rüdiger (2005) by substituting and , and defining : where L is a length scale corresponding to large-scale inhomogeneity. Assuming L = L d and l corr = l gives l corr / L d = l/ L = k 1 / k f ≈ 0.1, allowing Eq. ( 49 ) to be solved with b as an input from simulations. The maximum anisotropy used in the bulk of the simulations is A V ≈ 0.52, which yields b ≈ 2.1 and a ≈ 2.7. This is somewhat greater than the values used in the fitting above. However, this discrepancy is mostly due to the freedom in choosing the value of ν t . 4.4. Dependence of Λ effect on Reynolds number The simulations in the preceding sections were made at low Reynolds numbers in comparison to the astrophysically relevant regime. Figure 6 shows the Λ coefficients for a representative case where the Coriolis number (Ω ⋆ ≈ 1.0) and turbulence anisotropy ( A V ≈ 0.3) were fixed in the range Re ≈ 0.6...99. The Coriolis number was chosen such that the higher-order coefficients V (1) , V (2) , H (2) , and M (2) did not appear according to the criteria in Sect. 3.3 . At low Reynolds numbers Re = 0.6...2 all of the coefficients are proportional to Re as expected from mean-field theory. At low Re the error bars for H (1) and M (0, 1) increase because the mean values of Q x y and Q x z are small. Furthermore, the coefficients level off beyond Re ≳ 10 where they are consistent with constants although with large error bars in particular for H (1) . These results suggest that the results obtained at Re ≈10 are representative of what can be expected in more turbulent cases. 4.5. Influence of large-scale magnetic fields Dynamically significant magnetic fields are ubiquitous in astrophysical objects where the Λ effect is thought to be important. In particular, stars with convection zones harbour dynamos that produce magnetic fields on various scales. The effects of large-scale magnetic fields on the Λ effect have been studied analytically by Kitchatinov et al. (1994b) and Kitchatinov (2016) . These studies indicate that large-scale magnetic fields tend to quench the Λ effect, but also that an additional H (0) effect arises in the presence of a horizontal mean magnetic field. Here the study of Kitchatinov et al. (1994b) is followed where the quenching formulae for V (0) and H (0) were calculated as functions of the magnetic field assuming the field to be horizontal. They found that where β = B 0 / B eq , and These equations correspond to the case where the