Mean field dynamo action in shearing flows. II: fluctuating kinetic helicity with zero mean

TL;DR

This paper investigates how temporal fluctuations in kinetic helicity influence large-scale magnetic field generation in shearing flows, revealing conditions for dynamo growth and the effects of shear rate on dynamo characteristics.

Contribution

It extends previous work by analyzing the impact of fluctuating kinetic helicity with zero mean on dynamo action in shearing flows, using stochastic models with finite correlation times.

Findings

Growth occurs when helicity fluctuation timescale exceeds velocity fluctuation timescale.

Growth rate and dominant wavenumber exhibit non-monotonic dependence on shear rate.

Cycle period inversely proportional to shear at low shear, with collapse of curves for different parameters.

Abstract

Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in presence of a background linear shear flow. Key techniques involved here are same as in our earlier work \citep[][hereafter paper~I]{JS20}, 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, characterised 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 on 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 $k_\ast$ corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with $|S|$, with $k_\ast$ being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length scales. The cycle period $P_{\rm cyc}$ of growing dynamo wave is inversely proportional to $|S|$ at small shear, exactly as in the fixed kinetic helicity case of paper~I. 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 $m P_{\rm cyc}$ with $|S|$.