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, τ and τh, respectively. Growing solutions are obtained when τh > τ, even when this time-scale separation, characterized by m = τh/τ, remains below the threshold for causing the turbulent diffusion to turn negative. In regimes when turbulent diffusion remains positive, and τ is of the order of eddy turnover time T, the axisymmetric modes display non-monotonic behaviour with shear rate S: both, the growth rate γ and the wavenumber k* corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with |S|, with k* being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length-scales. The cycle period Pcyc of growing dynamo wave is inversely proportional to |S| 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 mPcyc with |S|.