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11.
B. R. Durney 《Solar physics》1975,41(1):233-240
The gas-magnetic field interaction of an isothermal axisymmetric corona is considered. A method is suggested for solving the MHD equations in the case when a uniform gas pressure and the radial component of the magnetic field (as in a dipole) are specified at the Sun's surface. The flux of open field lines (φ) can be given arbitrarily, and no reconnection or opening of field lines can take place. If configurations in hydrostatic equilibrium between the regions of open and closed field lines can be found, then the method of solution converges. The equation of hydrostatic equilibrium at the neutral point (assumed to be of the T-type) is written in a simple form, and it is shown that if φ is smaller than a certain φmin, this equation cannot be satisfied. Configurations in hydrostatic equilibrium between the regions of open and closed field lines are expected to exist for any value of φ larger than φmin. 相似文献
12.
B. R. Durney 《Solar physics》1973,30(1):223-234
The two-fluid equations for the solar wind are written down in a simplified form, similar to that suggested by Roberts (1971) for the one-fluid model. The equations are shown to depend only on one parameter, $$K = GM\kappa _e m_p (\varepsilon _\infty T_0 )^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} /4k^2 Fe,$$ , where G is the gravitational constant, M the mass of the star, κ e the thermal electron conductivity, m p the proton mass, k the Boltzman constant, k? ∞T0 the residual energy per particle at infinity and F e the electron-particle flux. For a variety of values of the density and temperature at the base of the corona we compute the solutions of the two-fluid solar wind model and compare the predicted and observed solar wind parameters at the Earth. 相似文献
13.
14.
15.
Bernard R. Durney 《Solar physics》1996,166(2):231-260
In a previous paper (Paper I), we studied a dynamo model of the Babcock-Leighton type (i.e., the surface eruptions of toroidal magnetic field are the source for the poloidal field) that included a thin, deep seated, generating layer (GL) for the toroidal field, B. Meridional motions (of the order of 12 m s–1 at the surface), rising at the equator and sinking at the poles were essential for the dynamo action. The induction equation was solved by approximating the latitudinal dependence of the fields by Legendre polynomials. No solutions were found with
p
=
f
where
p
and
f
are the fluxes for the preceding and following spot, respectively. The solutions presented in Paper I, had
p
= –0.5
f
, were oscillatory in time, and large radial fields, B, were present at the surface.Here, we resume the study of Paper I with a different numerical approach allowing for a much higher resolution in , the polar angle. The time dependent partial differential equations for the toroidal and poloidal field are solved with the help of a second order, time and space centered, finite difference scheme. Oscillatory solutions with
p
=
f
are found for various values of the meridional motions and diffusivity coefficients. The surface values of B, while considerably smaller than those of Paper I, are still unacceptably large, specially at the poles. The reason can be traced to the eruption of toroidal field at high latitudes. It appears that in order to obtain small values for the radial field in the polar regions, high latitude sources ( smaller than /4, say), must reach their maximum below the surface. Weaker meridional motions near the poles than in the equatorial region are also suggested. 相似文献
16.
By applying the principles of residence time distribution, the fundamental theorem of Cascadography states that a set of particles with identical residence times with exit a Cascadograph in a cluster. Since the validity of all Cascadographs depends on the accuracy of this theorem, it must be experimentally verified. This theorem was experimentally proven for the first time in a working Cascadograph. 相似文献
17.
The integrals, Ii(t) = GL ui
j × B
i
dv over the volume GL are calculated in a dynamo model of the Babcock–Leighton type studied earlier. Here, GL is the generating layer for the solar toroidal magnetic field, located at the base of the solar convection zone (SCZ); i=r, , , stands for the radial, latitudinal, and azimuthal coordinates respectively; j = (4)-1
× B, where B is the magnetic field; ur,u are the components of the meridional motion, and u is the differential rotation. During a ten-year cycle the energy cycle I(t)dt needs to be supplied to the azimuthal flow in the GL to compensate for the energy losses due to the Lorentz force. The calculations proceed as follows: for every time step, the maximum value of |B| in the GL is computed. If this value exceeds Bcr (a prescribed field) then there is eruption of a flux tube that rises radially, and reaches the surface at a latitude corresponding to the maximum of |B| (the time of rise is neglected). This flux tube generates a bipolar magnetic region, which is replaced by its equivalent axisymmetric configuration, a magnetic ring doublet. The erupted flux can be multiplied by a factor Ft, i.e., by the number of eruptions per time step. The model is marginally stable and the ensemble of eruptions acts as the source for the poloidal field. The arbitrary parameters Bcr and Ft are determined by matching the flux of a typical solar active region, and of the total erupted flux in a cycle, respectively. If E(B) is the energy, in the GL, of the toroidal magnetic field B = B sin cos , B (constant), then the numerical calculations show that the energy that needs to be supplied to the differential rotation during a ten-year cycle is of the order of E(Bcr), which is considerably smaller than the kinetic energy of differential rotation in the GL. Assuming that these results can be extrapolated to larger values of Bcr, magnetic fields 104 G, could be generated in the upper section of the tachocline that lies below the SCZ (designated by UT). The energy required to generate these 104 G fields during a cycle is of the order of the kinetic energy in the UT. 相似文献
18.
Bernard R. Durney 《Solar physics》2000,196(1):1-18
The torsional oscillations at the solar surface have been interpreted by Schüssler and Yoshimura as being generated by the Lorentz force associated with the solar dynamo. It has been shown recently that they are also present in the upper half of the solar convection zone (SCZ). With the help of a solar dynamo model of the Babcock–Leighton type studied earlier, the longitudinal component of the Lorentz force, L
, is calculated, and its sign or isocontours, are plotted vs. time, t, and polar angle, (the horizontal and vertical axis respectively). Two cases are considered, (1) differential rotation differs from zero only in the tachocline, (2) differential rotation as in (1) in the tachocline, and purely latitudinal and independent of depth in the bulk of the SCZ. In the first case the sign of L
is roughly independent of latitude (corresponding to vertical bands in the t, plot), whereas in the second case the bands show a pole–equator slope of the correct sign. The pattern of the bands still differs, however, considerably from that of the helioseismic observations, and the values of the Lorentz force are too small at low latitudes. It is all but certain that the toroidal field that lies at the origin of the large bipolar magnetic regions observed at the surface, must be generated in the tachocline by differential rotation; the regeneration of the corresponding poloidal field, B
p has not yet been fully clarified. B
p could be regenerated, for example, at the surface (as in Babcock–Leighton models), or slightly above the tachocline, (as in interface dynamos). In the framework of the Babcock-Leighton models, the following scenario is suggested: the dynamo processes that give rise to the large bipolar magnetic regions are only part of the cyclic solar dynamo (to distinguish it from the turbulent dynamo). The toroidal field generated locally by differential rotation must contribute significantly to the torsional oscillations patterns. As this field becomes buoyant, it should give rise, at the surface, to the smaller bipolar magnetic regions as, e.g., to the ephemeral bipolar magnetic regions. These have a weak non-random orientation of magnetic axis, and must therefore also contribute to the source term for the poloidal field. Not only the ephemeral bipolar regions could be generated in the bulk of the SCZ, but many of the smaller bipolar regions as well (at depths that increase with their flux), all contributing to the source term for the poloidal field. In contrast to the butterfly diagram that provides only a very weak test of dynamo theories, the pattern of torsional oscillations has the potential of critically discriminating between different dynamo models. 相似文献
19.
The relation between the average magnetic fieldB, the angular velocity , and the periodP of stellar activity cycles is studied. For the calculations we have used Leighton's (1969) model for the solar cycle with the additional assumption that the differential rotation and the cyclonic turbulence (Parker, 1955) (that is the sunspot tilt or the -effect) are both proportional to . We then find thatB is roughly proportional to and thatP decreases with increasing . The period of the solar cycle increases therefore with the age of the Sun.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
20.
Bernard R. Durney 《Solar physics》1995,160(2):213-235
A dynamo model of the Babcock-Leighton type having the following features is studied. The toroidal fieldB
is generated in a thin layer (the GL), located at the lower solar convection zone, by a shear in the angular velocity acting on the poloidal fieldB
p
(= × [0, 0,A
].) If, in this layer, and for a certain value of the polar angle,, |B
Ø
| exceeds a critical field,B
cr
, then the eruption of a flux tube occurs. This flux tube, which is assumed to rise radially, generates, when reaching the surface, a bipolar magnetic region (BMR) with fluxes
p
and
f
for the preceding and following spot respectively. For the purpose of the numerical calculations this BMR is replaced by its equivalent axisymmetrical magnetic ring doublet. The ensemble of these eruptions acts as the source term for the poloidal field. This field, generated in the surface layers, reaches the lower solar convection by transport due to meridional motions and by diffusion. The meridional motions are the superpositions of a one-cell velocity field that rises at the equator and sinks at the poles and of a two-cell circulation that rises at the equator and poles and sinks at mid latitudes. The toroidal field andA
Ø
were expanded in Legendre polynomials, and the coupled partial differential equations (int andr; time and radial coordinate) satisfied by the coefficients in these expansions were solved by a finite difference method. In the expansions, Legendre polynomials up to order thirty were included.In spite of an exhaustive search no solutions were found with
p
= –
f
. The solutions presented in this paper were obtained with p = –0.5
f
. In this case, the northern and southern hemisphere are not entirely decoupled since lines of force join both hemispheres. Most of the solutions found were periodic. For the one-cell meridional flow described above and for a purely radial shear in the GL (the angular velocity increasing inwards) the dynamo wave propagates from the pole towards the equator. The new cycle starts at the poles while the old cycle is still present in the equatorial regions. 相似文献