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 non-zero correlation time (τ). We use plane shearing waves in terms of time-dependent exact solutions to the Navier–Stokes equation as derived by Singh & Sridhar (2017). This allows us to self-consistently 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 (Pcyc) of the mean magnetic field. Both, γ and the wavenumber corresponding to the fastest growing axisymmetric mode vary non-monotonically 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 (Pcyc) of growing dynamo wave scales with shear as Pcyc ∝ |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 α2Ω) dynamo as also the α effect is affected by shear and the modelled random flow has a finite memory.

Various scenarios for the equatorward migration of sunspots

The profile of the differential rotation together with the sign of the alpha-effect determine the dynamo wave direction. In early models of the solar dynamo the dynamo wave often leads to a poleward migration of the activity belts. Flux transport by the meridional flow or the effect of the surface shear layer are possible solutions. In a model including the corona, we show that various migrations can be obtained by varying the properties of the corona. A new dynamo of Babcock-Leighton type also leads to the correct equatorward migration by the non-linear relation between flux density and rise time of the flux.

Dynamo cycles in global convection simulations of solar-like stars

Context. Several solar-like stars exhibit cyclic magnetic activity similar to the Sun as found in photospheric and chromospheric emission.Aims. We seek to understand the physical mechanism involved in rotational dependence of these activity cycle periods.Methods. We used three-dimensional magnetohydrodynamical simulations of global convective dynamos models of solar-like stars to investigate the rotational dependency of dynamos. We further applied the test-field method to determine theαeffect in these simulations.Results. We find dynamos with clear oscillating mean magnetic fields for moderately and rapidly rotating runs. For slower rotation, the field is constant or exhibit irregular cycles. In the moderately and rapidly rotating regime the cycle periods increase weakly with rotation. This behavior can be well explained with a Parker–Yoshimura dynamo wave traveling equatorward. Even though theαeffect becomes stronger for increasing rotation, the shear decreases more steeply, causing this weak dependence on rotation. Similar to other numerical studies, we find no indication of activity branches that have been postulated in former observational studies. However, our simulations seem to agree more with the transitional branch suggested by more recent observational studies. If the Sun exhibited a dynamo wave similar to that which we find in our simulations, it would operate deep inside the convection zone.

Role of longitudinal activity complexes for solar and stellar dynamos

In this paper we first discuss observational evidence of longitudinal concentrations of magnetic activity in the Sun and rapidly rotating late-type stars with outer convective envelopes. Scenarios arising from the idea of rotationally influenced anisotropic convective turbulence being the key physical process generating these structures are then presented and discussed - such effects include the turbulent dynamo mechanism, negative effective magnetic pressure instability (NEMPI) and hydrodynamical vortex instability. Finally, we discuss non-axisymmetric stellar mean-field dynamo models, the results obtained with them, and compare those with the observational information gathered up so far. We also present results from a pure α2 mean-field dynamo model, which show that time-dependent behavior of the dynamo solutions can occur both in the form of an azimuthal dynamo wave and/or oscillatory behavior related to the alternating energy levels of the active longitudes.