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تسجيل مستخدم جديدThe Effects of Rotation on the Evolution of Rising Omega-loops in a Stratified Model Convection Zone
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We present three-dimensional MHD simulations of buoyant magnetic flux tubes that rise through a stratified model convection zone in the presence of solar rotation. The equations of MHD are solved in the anelastic approximation, and the results are used to determine the effects of solar rotation on the dynamic evolution an Omega-loop. We find that the Coriolis force significantly suppresses the degree of fragmentation at the apex of the loop during its ascent toward the photosphere. If the initial axial field strength of the tube is reduced, then, in the absence of forces due to convective motions, the degree of apex fragmentation is also reduced. We show that the Coriolis force slows the rise of the tube, and induces a retrograde flow in both the magnetized and unmagnetized plasma of an emerging active region. Observationally, we predict that this flow will appear to originate at the leading polarity, and will terminate at the trailing polarity.
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We present three-dimensional numerical simulations of the rise and fragmentation of twisted, initially horizontal magnetic flux tubes which evolve into emerging Omega-loops. The flux tubes rise buoyantly through an adiabatically stratified plasma tha
t represents the solar convection zone. The MHD equations are solved in the anelastic approximation, and the results are compared with studies of flux tube fragmentation in two dimensions. We find that if the initial amount of field line twist is below a critical value, the degree of fragmentation at the apex of a rising Omega-loop depends on its three-dimensional geometry: the greater the apex curvature of a given Omega-loop, the lesser the degree of fragmentation of the loop as it approaches the photosphere. Thus, the amount of initial twist necessary for the loop to retain its cohesion can be reduced substantially from the two-dimensional limit. The simulations also suggest that as a fragmented flux tube emerges through a relatively quiet portion of the solar disk, extended crescent-shaped magnetic features of opposite polarity should form and steadily recede from one another. These features eventually coalesce after the fragmented portion of the Omega-loop emerges through the photosphere.
We present results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong m
eridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the {it thermodynamics controls the dynamics through the Taylor-Proudman momentum balance}. The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity `bump.
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A couple
d system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral tau approach which is valid for large Reynolds and Peclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.
A magnetic flux tube may be considered both as a separate body and as a confined field. As a field, it is affected both by the cyclonic convection ($alpha$-effect) and differential rotation ($Omega$-effect). As a body, the tube experiences not only a
buoyant force, but also a dynamic pressure due to downflows above the tube. When these two dynamic effects are incorporated into the $alphaOmega$ dynamo equations, we obtain a dynamo operating in the convection zone. We analyze and solve the extended dynamo equations in the linear approximation by using observed solar internal rotation and assuming a downflow suggested by numerical simulations of the solar convection zone. The results produce: (i) the 22-year cycle period; (ii) the extended butterfly diagram; (iii) the confinement of strong activity to low heliographic latitudes $|Phi|le 35^circ$; (iv) at low latitudes the radial field is in an approximately $pi$ phase lag compared to the toroidal field at the same latitude; (v) the poleward branch is in a $pi/2$ phase lag with respect to the equatorward branch; (vi) most of the magnetic flux is present in a strongly intermittent form, concentraed into strong flux tubes; (vii) the magnetic field peaks at a depth of $r=0.96 R_{sun}$; (viii) total solar irradiance varies in phase with the solar cycle activity, having an amplitude of 0.1%; (ix) solar effective temperature varies in phase with the solar cycle activity, having an amplitude of 1.5 $^circ C$; and (x) solar radius also varies in phase with the solar cycle activity, having an amplitude of 20 mas. All these results are in agreement with the corresponding observations.
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Alberto Bigazzi
, Alexander A. Ruzmaikin (Jet Propulsion Laboratory
, n California Institute of Technology
2002
One of the key questions in solar physics that remains to be answered concerns the strength and the distribution of the magnetic fields at the base of the convection zone. The flux tube dynamics requires that toroidal fields of strength as large as 1
00 kilogauss be present at the base of the convection zone. The kinetic-magnetic equipartition argument leads to smaller field strengths. For possible detection of these relatively small (compared to pressure effects) fields by helioseismic methods it is important to know the range of the field strengths and their distribution. We estimate a range for the toroidal magnetic field strengths at the base of the convection zone using dynamo simulations in a spherical shell. These simulations involve the distribution of rotation provided by helioseismic
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