Virtual Nordic Dynamo Seminar

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

by Hongzhe Zhou (Nordita)


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 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 (βu21) and magnetic (βb21) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike βb21, the kinetic SCE βu21 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, βb21 is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive βu21 can dominate even at energy equipartition urmsbrms, resulting in a positive total β21 even though βb21<0. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation (SOCA) versus the spectral-τ closure (STC), for which opposite signs for βu21 have been reported, with the same sign for βb21<0. The results also offer an explanation for the simulations that find βu21>0 and an inconclusive overall sign of β21 for O(10) Reynolds numbers. The transient behavior of βu21 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.