Mean field dynamo action in shear flows. I: fixed kinetic helicity
Abstract
We study mean field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and nonzero correlation time (τ). We use plane shearing waves in terms of timedependent exact solutions to the NavierStokes equation as derived by Singh & Sridhar (2017). This allows us to selfconsistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues that yield the growth rate (γ) and the cycle period (P_{cyc}) of the mean magnetic field. Both, γ and the wavenumber corresponding to the fastest growing axisymmetric mode vary nonmonotonically with shear rate S when τ is comparable to the eddy turnover time T, in which case, we also find quenching of dynamo when shear becomes too strong. When $\tau /T\sim {\cal O}(1)$ , the cycle period (P_{cyc}) of growing dynamo wave scales with shear as P_{cyc} ∝ S^{1} at small shear, and it becomes nearly independent of shear as shear becomes too strong. This asymptotic behaviour at weak and strong shear has implications for magnetic activity cycles of stars in recent observations. Our study thus essentially generalizes the standard αΩ (or α^{2}Ω) dynamo as also the α effect is affected by shear and the modelled random flow has a finite memory.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 July 2020
 DOI:
 10.1093/mnras/staa1204
 arXiv:
 arXiv:1911.00235
 Bibcode:
 2020MNRAS.495.4557J
 Keywords:

 dynamo;
 magnetic fields;
 MHD;
 plasmas;
 turbulence;
 stars: activity;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Fluid Dynamics
 EPrint:
 16 pages, 9 figures, accepted for publication in MNRAS