| Dynamics of the fast solar tachocline II. Migrating field |
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We present detailed numerical calculations of the fast solar tachocline arising
from the assumption that the turbulent diffusivity in the tachocline region exceeds
eta>109 cm2/s. In this case, the dynamo field dominates
the dynamics of the tachocline. In the present paper of the series,
we study the influence of a migrating magnetic field
on the penetration of the differential rotation into the radiative region. The migrating
field is prescribed as the observed axisymmetric radial magnetic field (Stenflo, 1988, 1994).
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| Dynamics of the fast solar tachocline I. Dipolar field |
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One possible scenario for the origin of the solar tachocline, known as the
"fast tachocline", assumes that the turbulent diffusivity exceeds eta>
109 cm2/s. In this case the dynamics will be governed by the
dynamo-generated oscillatory magnetic field on relatively short timescales.
Here, for the first time, we present detailed numerical models for the fast
solar tachocline with all components of the magnetic field calculated
explicitly, assuming axial symmetry and a constant turbulent diffusivity eta
and viscosity nu.
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| Torsinal Oscillations in the Solar Convection Zone |
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We present a model for torsional oscillations where the inhibiting effect of
active region magnetic fields on turbulence locally reduces turbulent viscous
torques, leading to a cycle- and latitude-dependent modulation of the
differential rotation. The observed depth dependence of torsional oscillations
as well as their phase relationship with the sunspot butterfly diagram are
reproduced quite naturally in this model. The resulting oscillation amplitudes
are significantly smaller than observed, though
they depend rather sensitively on model details. Meridional circulation is
found to have only a weak effect on the oscillation pattern.
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| The Thin Tachocline Problem |
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Helioseismic measurements indicate that the solar tachocline is very thin, its
full thickness not exceeding 4% of the solar radius. The reason for this is
not known. We have demonstrated that the tachocline can be confined to its
observed thickness by a poloidal magnetic field of about one kilogauss,
penetrating below the convective zone and oscillating with a period of 22
years, if the tachocline region is turbulent with a diffusivity of
eta~1010 cm2/s. A similar confinement may be produced
for other pairs of the parameter values (Bp, eta).
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| Asymmetric Shape of the Magnetic Flux Loops in Active Regions |
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In 1990 we pointed out that an asymmetry of the magnetic flux loops can readily
explain many observed peculiarities of of active regions, most importantly to
the characteristic proper motion pattern of sunspots. We predicted, and
afterwards demonstrated from observations an asymmetric, eastward shifted
position of the magnetic 0-line (the "magnetic equator" of active regions)
compared to the main spots. A few years later our results attracted great
international interest as an asymmetry similar to what we predicted was found
in flux emergence calculations.
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| Discovery of the Decay Law of Sunspots |
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For centuries, astronomers observed the decay of sunspots, but the great
individual differences and vagaries in the behaviour of spots did not make it
possible to derive the statistical law governing the decay process. Lacking a
better method, the decay was usually crudely described as a linear decrease of
the spot area with time. A few years ago we constructed the first model of
sunspot decay that agrees with all the basic empirical facts, the so-called
turbulent erosion model. This model yielded a well-determined parabolic law for
sunspot decay. We could confirm this prediction beyond doubt by an analysis of
available observational material. This finally settles the age-old problem of
the sunspot decay law.
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| The Convective Zone as a "Steamy Window" |
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For an understanding of just how the solar dynamo works it would be important to
know to what extent the processes going on in the convective zone and
photosphere participate in the generation and transport of magnetic fields. To
study this problem, we developed a 2-dimensional, axisymmetric, time-dependent
model for the transport of the weak large-scale solar magnetic field (outside
active regions). Our results show that the convective zone plays a passive role,
acting as a "steamy window" through which we observe a fuzzy image of the
magnetic field structure generated at the bottom of the convective zone.
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| Modelling the Turbulent Magnetic Field of the Sun |
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Beside the weak, large scale magnetic field of 1-2 G, a small-scale magnetic
field is also present throughout the solar surface. This consists of elements of
mixed polarity, and its full flux density exceeds that of the larg-scale field
by an order of magnitude. We pointed out that the most plausible interpretation
of the origin of this field is a small-scale dynamomechanism operative in the
photosphere, and we constructed a detailed model for the height dependence and
for the spatiotemporal fluctuations of the flux density of this turbulent field.
The results are in agreement with observations.
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| Studies of the Morphology of Turbulent Convection |
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We developed a detailed model for homogeneous, anisotropic
turbulent convection at low Prandtl-numbers (i.e. at low viscosity and high
temperatures, as is the case in stars). Contrary to some earlier assumptions,
the anisotropy (i.e. the ratio of horizontal and vertical velocities) proved to
be moderate (order of unity) even for high Rayleigh numbers (for very violent
convection). We further showed that the morphological characteristics of
convection known from numerical simulations (asymmetry of up- and downflows,
"plumes") can also be predicted on the basis of the Reynolds momentum equations
of hydrodynamics.
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