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Register a new userResonances for activity waves in spherical mean field dynamos
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We study activity waves of the kind that determine cyclic magnetic activity of various stars, including the Sun, as a more general physical rather than a purely astronomical problem. We try to identify resonances which are expected to occur when a mean-field dynamo excites waves of quasi-stationary magnetic field in two distinct spherical layers. We isolate some features that can be associated with resonances in the profiles of energy or frequency plotted versus a dynamo governing parameter. Rather unexpectedly however the resonances in spherical dynamos take a much less spectacular form than resonances in many more familiar branches of physics. In particular, we find that the magnitudes of resonant phenomena are much smaller than seem detectable by astronomical observations, and plausibly any related effects in laboratory dynamo experiments (which of course are not in gravitating spheres!) are also small. We discuss specific features relevant to resonant phenomena in spherical dynamos, and find parametric resonance to be the most pronounced type of resonance phenomena. Resonance conditions for these dynamo wave resonances are rather different from those for more conventional branches of physics. We suggest that the relative insignificance of the phenomenon in this case is because the phenomena of excitation and propagation of the activity waves are not well-separated from each other and this, together with the nonlinear nature of more-or-less realistic dynamos, suppress the resonances and makes them much less pronounced than resonant effects, for example in optics.
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When scale separation in space and time is poor, the alpha effect and turbulent diffusivity have to be replaced by integral kernels. Earlier work in computing these kernels using the test-field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean-field equations are solved for oscillatory alpha-shear dynamos as well as alpha^2 dynamos in which alpha is antisymmetric about the equator, making this dynamo also oscillatory. In both cases, the critical values of the dynamo number is lowered by the fact that the dynamo is oscillatory.
We study the connection between spherical wedge and full spherical shell geometries using simple mean-field $alpha^2$ dynamos. We solve the equations for a one-dimensional time-dependent mean-field dynamo to examine the effects of varying the polar angle $theta_0$ between the latitudinal boundaries and the poles in spherical coordinates. We investigate the effects of turbulent magnetic diffusivity and $alpha$ effect profiles as well as different latitudinal boundary conditions to isolate parameter regimes where oscillatory solutions are found. Finally, we add shear along with a damping term mimicking radial gradients to study the resulting dynamo regimes. We find that the commonly used perfect conductor boundary condition leads to oscillatory $alpha^2$ dynamo solutions only if the wedge boundary is at least one degree away from the poles. Other boundary conditions always produce stationary solutions. By varying the profile of the turbulent magnetic diffusivity alone, oscillatory solutions are achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By introducing radial shear and a damping term mimicking radial gradients, we again see oscillatory dynamos, and the direction of drift follows the Parker--Yoshimura rule. Oscillatory solutions in the weak shear regime are found only in the wedge case with $theta_0 = 1^circ$ and perfect conductor boundaries. A reduced $alpha$ effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and reproduces best the solutions in spherical wedges.
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 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.
(abidged) Context: Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and 5, respectively). Results: We find that the rotation profiles for high thermal diffusivity show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased. This coincides with a change in the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the cyclic solutions disappear at the highest magnetic Reynolds numbers. The total magnetic energy increases with the magnetic Reynolds number in the range studied here ($5-151$), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases we find that two regimes are possible where either differential rotation is strong and mean magnetic fields relatively weak or vice versa. Conclusions: Our simulations indicate a strong non-linear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients.
We study magnetic field evolution in flows with fluctuating in time governing parameters in electrically conducting fluid. We use a standard mean-field approach to derive equations for large-scale magnetic field for the fluctuating ABC-flow as well as for the fluctuating Roberts flow. The derived mean-field dynamo equations have growing solutions with growth rate of the large-scale magnetic field which is not controlled by molecular magnetic diffusivity. Our study confirms the Zeldovich idea that the nonstationarity of the fluid flow may remove the obstacle in large-scale dynamo action of classic stationary flows.
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