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

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 $P_{\mathrm{cyc}}$ 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 $m{P}_{\mathrm{cyc}}$ with $|S|$.

arXiv comment14 pages, 10 figures, Submitted to MNRAS

References in corpus (26)

• Astrophysical magnetic fields and nonlinear dynamo theory
• Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence
• An Incoherent $\alpha -\Omega$ Dynamo in Accretion Disks
• Generation of Magnetic Field by Combined Action of Turbulence and Shear
• Large-Scale Magnetic-Field Generation by Randomly Forced Shearing Waves
• Numerical experiments on dynamo action in sheared and rotating turbulence
• Generation of large-scale magnetic fields by small-scale dynamo in shear flows
• Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear
• Scaling and intermittency in incoherent α-shear dynamo
• Numerical study of large-scale vorticity generation in shear-flow turbulence
• The shear dynamo problem for small magnetic Reynolds numbers
• Effect of Rotation on a Developed Turbulent Stratified Convection: the Hydrodynamic Helicity, the Alpha-Effect and the Effective Drift Velocity
• Nonperturbative quasilinear approach to the shear dynamo problem
• Large-scale dynamo action due to $\alpha$ fluctuations in a linear shear flow
• Transport coefficients for the shear dynamo problem at small Reynolds numbers
• Shear dynamo problem: Quasilinear kinematic theory
• Turbulent transport coefficients in galactic dynamo simulations using singular value decomposition
• The Elemental Shear Dynamo
• Numerical studies of dynamo action in a turbulent shear flow - I
• Nonhelical mean-field dynamos in a sheared turbulence
• On the existence of shear-current effects in magnetized burgulence
• Moffatt drift driven large scale dynamo due to $\alpha$ fluctuations with nonzero correlation times
• Mean field dynamo action in renovating shearing flows
• Generation of large-scale magnetic fields due to fluctuating $\alpha$ in shearing systems
• Mean field dynamo action in shear flows. I: fixed kinetic helicity
• Plane shearing waves of arbitrary form: exact solutions of the Navier-Stokes equations

Cited by in corpus (1)

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