Solar magnetic activity shows both smooth secular changes, such as the Grand Modern Maximum, and quite abrupt drops that are denoted as Grand Minima. Direct numerical simulations (DNS) of convection driven dynamos offer one way of examining the mecha
nisms behind these events. In this work, we analyze a solution of a solar-like DNS that has been evolved for roughly 80 magnetic cycles of 4.9 years, during which epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. The DNS employed is a semi-global (wedge) magnetoconvection model. For data analysis we use Ensemble Empirical Mode Decomposition (EEMD) and phase dispersion ($D^2$) methods. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like. This mode is accompanied by a higher frequency mode near the surface and a low-frequency mode in the bottom of the convection zone. The overall behavior of the dynamo solution is very complex exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum. We interpret the overall irregular behavior to be due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses.
We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun. We solve the compressible magnetohydrodynamic equations
in a two-layer model with unstable stratification below the surface, representing the convection zone, and a stably stratified coronal envelope above. The interface represents a free surface. We compare our model to models that have no coronal envelope. The presence of a coronal envelope is found to modify the Reynolds stress and the $Lambda$ effect resulting in a weaker and non-cylindrical differential rotation. This is related to the reduced latitudinal temperature variations that are caused by and dependent on the angular velocity. Some simulations develop a near-surface shear layer that we can relate to a sign change in the meridional Reynolds stress term in the thermal wind balance equation. Furthermore, the presence of a free surface changes the magnetic field evolution since the toroidal field is concentrated closer to the surface. In all simulations, however, the migration direction of the mean magnetic field can be explained by the Parker--Yoshimura rule, which is consistent with earlier findings. A realistic treatment of the upper boundary in spherical dynamo simulations is crucial for the dynamics of the flow and magnetic field evolution.
We present results from four convectively-driven stellar dynamo simulations in spherical wedge geometry. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons we show that the migration direction can
be explained by an $alphaOmega$ dynamo wave following the Parker--Yoshimura rule. We conclude that the equatorward migration in this and previous work is due to a positive (negative) $alpha$ effect in the northern (southern) hemisphere and a negative radial gradient of $Omega$ outside the inner tangent cylinder of these models. This idea is supported by a strong correlation between negative radial shear and toroidal field strength in the region of equatorward propagation.
We report the finding of an azimuthal dynamo wave of a low-order (m=1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean field dynamo theory and have been obtained previously in m
ean-field models. Observational results both from photometry and Doppler imaging have revealed persistent drifts of spots for several rapidly rotating stars, but, although an azimuthal dynamo wave has been proposed as a possible mechanism responsible for this behavior, it has been judged as unlikely, as practical evidence for such waves from DNS has been lacking. The large-scale magnetic field in our DNS, which is due to self-consistent dynamo action, is dominated by a retrograde m=1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m=1 structures coincide reasonably with the maxima of m=2 structures of the temperature. These results provide direct support for the observed drifts being due to an azimuthal dynamo wave.
We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification
is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about 3-7 times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about $pi/2$, which can be explained by an oscillatory $alpha^2$ dynamo caused by the sign change of the $alpha$-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an $m=1$ mode is excited for a full $2pi$ azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.
We report on the results of four convective dynamo simulations with an outer coronal layer. The magnetic field is self-consistently generated by the convective motions beneath the surface. Above the convection zone, we include a polytropic layer that
extends to 1.6 solar radii. The temperature increases in this region to $approx8$ times the value at the surface, corresponding to $approx1.2$ times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find solar-like differential rotation with radial contours of constant rotation rate, together with a near-surface shear layer. This non-cylindrical rotation profile is caused by a non-zero latitudinal entropy gradient that offsets the Taylor--Proudman balance through the baroclinic term. The meridional circulation is multi-cellular with a solar-like poleward flow near the surface at low latitudes. In most of the cases, the mean magnetic field is oscillatory with equatorward migration in two cases. In other cases, the equatorward migration is overlaid by stationary or even poleward migrating mean fields.
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 anis
otropic 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 alpha-squared 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.
We present results of convective turbulent dynamo simulations including a coronal layer in a spherical wedge. We find an equatorward migration of the radial and azimuthal fields similar to the behavior of sunspots during the solar cycle. The migratio
n of the field coexist with a spoke-like differential rotation and anti-solar (clockwise) meridional circulation. Even though the migration extends over the whole convection zone, the mechanism causing this is not yet fully understood.
We combine a convectively driven dynamo in a spherical shell with a nearly isothermal density-stratified cooling layer that mimics some aspects of a stellar corona to study the emergence and ejections of magnetic field structures. This approach is an
extension of earlier models, where forced turbulence simulations were employed to generate magnetic fields. A spherical wedge is used which consists of a convection zone and an extended coronal region to $approx1.5$ times the radius of the sphere. The wedge contains a quarter of the azimuthal extent of the sphere and $150degr$ in latitude. The magnetic field is self-consistently generated by the turbulent motions due to convection beneath the surface. Magnetic fields are found to emerge at the surface and are ejected to the coronal part of the domain. These ejections occur at irregular intervals and are weaker than in earlier work. We tentatively associate these events with coronal mass ejections on the Sun, even though our model of the solar atmosphere is rather simplistic.
In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions of the onset of the instability were investigated in terms of the
Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the co-latitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.
