Mean field dynamo action in shearing flows - II. Fluctuating kinetic helicity with zero mean

Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in the presence of a background linear shear flow. Key techniques involved here are same as in our earlier work, where we have used the renovating flow based model with shearing waves. Both the velocity and the helicity fields are treated as stochastic variables with finite correlation times, tau and tau(h), respectively. Growing solutions are obtained when tau(h) > tau, even when this time-scale separation, characterized by m = tau(h)/tau, remains below the threshold for causing the turbulent diffusion to turn negative. In regimes when turbulent diffusion remains positive, and tau is of the order of eddy turnover time T, the axisymmetric modes display non-monotonic behaviour with shear rate S: both, the growth rate gamma and the wavenumber k* corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with vertical bar S vertical bar, with k* being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length-scales. The cycle period P-cyc of growing dynamo wave is inversely proportional to vertical bar S vertical bar at small shear, exactly similar to the fixed kinetic helicity case of our earlier work. This dependence becomes shallower at larger shear. Interestingly enough, various curves corresponding to different choices of m collapse on top of each other in a plot of mP(cyc) with vertical bar S vertical bar.

Automated summary

In this study, we investigate the impact of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in the presence of a background linear shear flow. Our findings show that growing solutions can be obtained when the correlation time of helicity is greater than the correlation time of velocity. Interestingly, under certain conditions, the axisymmetric modes exhibit non-monotonic behavior in relation to shear rate.