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1.
In this paper we study the interaction of rotation with convection in a deep compressible spherical shell as the Sun's convection zone. We examine how the energy transport and the large scale motions can be affected by rotation. In particular we study how a large scale meridional circulation can give rise to variations of angular velocity with latitude and depth.It is assumed that the energy transport is only due to convection and that the mixing-length theory gives an adequate representation of it. Furthermore we assume that rotation acts as a perturbation of the turbulent convective flux through its transport coefficient.The equations involved in the model are integrated numerically in the limit of large viscosity and slow rotation. After having expanded all physical quantities to the first order in terms of Legendre polynomials, the fitting with the observed solar differential rotation gives the expansion parameter, which represents the coupling constant between rotation and convection.The results show a three-cell circulation extending from the poles to the equator. The first one is located in the lower half of the convection zone with the fluid rising at the equator and sinking at the poles. In the second one the direction of the motion is reversed while the third one, located in a thin upper layer, shows the same characteristics of the first one. The meridional velocities at the surface are directed towards the poles and are about 20 cm s-1. In the other cells the meridional velocities are typically of a few cm s-1 while the radial velocities are of the order of a few tenths of cm s-1.The heat flux relative variation at the surface is about 10-4 (3 × 10-3 at the bottom) with a polar excess. The temperature variation at the surface is of the same order, with an equatorial excess however. The convection seems to be stabilized stronger at the equator. The angular velocity increases inwards and varies about 6% between the surface and the bottom of the convection zone.An attempt is made for explaining the picture which emerges. In particular the negligible flux and temperature variations at the surface are explained in terms of equalization by the particular structure of the latitudinal flow. This configuration of large scale circulation is attributed to the high stratification of the convection zone with depth. 相似文献
2.
In this paper we study the dependence on depth and latitude of the solar angular velocity produced by a meridian circulation in the convection zone, assuming that the main mechanism responsible for setting up and driving the circulation is the interaction of rotation with convection. We solve the first order equations (perturbation of the spherically symmetric state) in the Boussinesq approximation and in the steady state for the axissymmetric case. The interaction of convection with rotation is modelled by a convective transport coefficient k c = k co + ?k c2 P 2(cos θ) where ? is the expansion parameter, P 2 is the 2nd Legendre polynomial and k c2 is taken proportional to the local Taylor number and the ratio of the convective to the total fluxes. We obtain the following results for a Rayleigh number 103 and for a Prandtl number 1:
- A single cell circulation extending from poles to the equator and with circulation directed toward the equator at the surface. Radial velocities are of the order of 10 cm s?1 and meridional ones of the order of 150 cm s?1.
- A flux difference between pole and equator at the surface of about 5 percent, the poles being hotter.
- An angular velocity increasing inwards.
- Angular velocity constant surfaces of spheroidal shape. The model is consistent with the fact that the interaction of convection with rotation sets up a circulation (driven by the temperature gradient) which carries angular momentum toward the equator against the viscous friction. Unfortunately also a large flux variation at the surface is obtained. Nevertheless it seems that the model has the basic requisites for correct dynamo action.
3.
We report on observations of global solar Ca K-line intensity oscillations taken in May 1991 from Mees Solar Observatory, Hawaii. We measurep-mode frequency splittings for modes of spherical harmonic degrees between 20 and 129 averaged over the radial order of the modes. Our measurement of the antisymmetric component of the splittings is comparable with previous measurements and thus indicates a decrease in the latitudinal differential rotation with depth into the convection zone and the upper radiative zone. We find evidence for a 1% variation in the rotation rate of the upper convection zone roughly in phase with the solar activity cycle. Our measurement of the symmetric component of the splittings is of the same order as was reported from the previous solar maximum and is an order of magnitude larger than has been measured near solar minimum. From the degree dependence of the symmetric component of the splittings, we find evidence for an aspherical fractional sound speed perturbation located at a depth of 0.85 ± 0.05 solar radii. This perturbation has a magnitude ofc/c +9 × 10–4 at the equator relative to the poles. Additionally, there is evidence for a near-surface aspherical sound speed perturbation of smaller magnitudec/c +4 × 10–4 at the equator relative to the poles. If an intense global magnetic field were the dominant source of the observed symmetric component of the splittings, instead of latitudinal gradients in the sound speed, then global fields of order 105 G would be required in the convection zone. 相似文献
4.
We report new results obtained from high precision computer controlled tracings of ca. 400 bright Ca+-mottles made during summer 1975 in continuation of our 1974 program (Schröter and Wöhl, 1975). In particular, we looked in 1975 for the existence of a giant circulation pattern in the equatorial zone. We find for the differential rotation: = 13.93 – 2.90 sin2
B (deg/day, sidereal) when combining the new measurements with those obtained in 1974. Observations from 26th April until June 19th give strong evidence that at that time four giant circulation cells, crossing the solar equator, (i.e. a nonaxisymmetric velocity field pattern with respect to the solar equator) did exist. This yields two more rapid and two slower rotating sectors with v = ±80 m s–1. These giant cells transport angular momentum towards the equator. 相似文献
5.
Thomas L. Duvall Jr. 《Solar physics》1979,63(1):3-15
Daily observations of Doppler line shifts made with very low spatial resolution (3) with the Stanford magnetograph have been used to study the equatorial rotation rate, limb effect on the disk, and the mean meridonial circulation. The equatorial rotation rate was found to be approximately constant over the interval May 1976–January 1977 and to have the value 2.82 rad s–1 (1.96 km s–1). This average compares favorably with the results of Howard (1977) of 2.83 rad s–1 for the same time period. The RMS deviation of the daily measurements about the mean value was 1% of the rate (20 m s–1), much smaller than the fluctuations reported by Howard and Harvey (1970) of several per cent. These 1% fluctuations are uncorrelated from day-to-day and may be due to instrumental problems. The limb effect on the disk was studied in equatorial scans (after suppressing solar rotation). A redshift at the center of the disk relative to a position 0.60R
from the center of 30 m s–1 was found for the line Fe i 5250 Å. Central meridian scans were used (after correcting for the limb effect defined in the equatorial scans) to search for the component of mean meridonial circulation symmetric across the equator. A signal is found consistent with a polewards flow of 20 m s–1 approximately constant over the latitude range 10–50°. Models of the solar differential rotation driven by an axisymmetric meridonial circulation and an anisotropic eddy viscosity (Kippenhahn, 1963; Cocke, 1967; Köhler, 1970) predict an equatorwards flow at the surface. However, giant cell convection models (Gilman, 1972, 1976, 1977) predict a mean polewards flow (at the surface). The poleward-directed meridonial flow is created as a by-product of the giant cell convection and tends to limit the differential rotation. The observation of a poleward-directed meridonial circulation lends strong support to the giant cell models over the anisotropic eddy viscosity models.Now at Kitt Peak National Observatory, Tucson, Ariz., U.S.A. 相似文献
6.
Peter A. Gilman 《Solar physics》1972,27(1):3-26
We present extensive numerical calculations for a model of thermal convection of a Boussinesq fluid in an equatorial annulus of a rotating spherical shell. The convection induces and maintains differential rotation and meridian circulation. The model is solved for an effective Prandtl number P = 1, with effective Taylor number T in the range 102 <T <106, and effective Rayleigh number R between the critical value for onset of convection, and a few times that value. With = 2.6 × 10–6 s–1, d = 1.4 × 1010 cm (roughly the depth of the solar convection zone) the range of Taylor number is equivalent to kinematic viscosities between 1014 and 1012 cm2 s–1, which encompasses eddy viscosities estimated from mixing length theory applied to the Sun.The convection does generally make equatorial regions rotate faster, the more so as T is increased, but local equatorial deceleration near the surface is also produced at intermediate T for large enough R above critical. The differential rotation is maintained primarily through momentum transport in the cells up the gradient, rather than by meridian circulation. Differential rotation energy increases relative to cell energy with increasing T, surpassing it near T = 3 × 104. The differential rotation tends to stretch out the convective cells, analogously to what is thought to happen to solar magnetic regions. Differential rotation and meridian circulation energies are nearly equal for T = 103, but the meridian circulation energy falls off relative to differential rotation like T
–1 for larger T. The meridian circulation is always toward the poles near the surface, contrary to models of Kippenhahn, Cocke, Köhler, and Durney and Roxburgh. The radial shear produced in the differential rotation is almost always positive, as in the Köhler model, but contrary to the assumptions made by Leighton for his random walk solar cycle model.Solutions in the neighborhood of T = 3 × 104 seem to compare best with various solar observations including differential rotation amplitude, cell wavelength, tilted structure, horizontal momentum transport, and weak meridian circulation. The local equatorial deceleration (equatorward of 10–15°) has not been observed, although the techniques of data analysis may not have been sensitive to it. The most important deficiency of the model is that all the solutions with T 103 show the vertical heat transport a rather strong function of latitude, with a maximum at the equator, no evidence of which is seen at the solar surface.The National Center for Atmospheric Research is sponsored by The National Science Foundation. 相似文献
7.
In a first order approximation the influence of meridional circulations in a spherical shell on the radial dependence of the angular velocity is studied. Due to stationarity the flux of angular momentum which is transported through any sphere by the circulations must be cancelled by the flux of angular momentum due to turbulent friction. If the circulation goes equatorward at the outer surface the law of rotation must be such that angular momentum is transported in outward direction through the sphere. 相似文献
8.
The sidereal rotation rate of the high-latitude solar regions is examined using long-lived photospheric polar faculae. The observations were carried out with the photoheliograph of Kislovodsk Mountain Station of the Pulkovo Observatory from 1982 to 1986. The following facts have been established: (a) There is a differential rotation of the polar faculae close to the maximum of solar activity, while the amount of latitude gradient of solar rotation decreases towards the sunspot minimum; (b) small differences of rotation in the northern and southern hemispheres of the Sun are observed; (c) some deviations of differential rotation curves constructed for each Carrington rotation from the mean curve of differential rotation are revealed. The total amplitude of the maximum positive and negative excesses is about 40–50 m s–1. The positive surplus velocities of solar rotation (the amplitude of which is about 20–25 m s–1) move in the form of a wave from heliographic latitudes 40° with a velocity of 1.6 m s–1. The latitude width of this flow is B 15°. This wave of abnormally high velocity starts in the year of minimum solar activity and reaches the pole 11 years later. The picture is symmetrical relative to the equator. 相似文献
9.
Standing wave torsional oscillations of wavenumber 1/2 and 1 hemisphere–1 are studied using an improved fit to Mount Wilson magnetograph data. These oscillations are seen to be in phase with each other and with the magnetic activity cycle, and seem best represented as a flexing of the differential rotation curve. Superposing them gives a differential rotation which at solar minimum is slightly flattened at the equator but considerably ( 5%) steepened at the poles, and also tends to produce a travelling wave with wavenumber 1 hemisphere–1 that moves from pole to equator as the cycle progresses. 相似文献
10.
We describe a method for the analysis of magnetic data taken daily at the Vacuum Telescope at Kitt Peak. In this technique, accurate position differences of very small magnetic features on the solar surface outside active regions are determined from one day to the next by a cross-correlation analysis. In order to minimize systematic errors, a number of corrections are applied to the data for effects originating in the instrument and in the Earth's atmosphere. The resulting maps of solar latitude vs central meridian distance are cross-correlated from one day to the next to determine daily motions in longitude and latitude. Some examples of rotation and meridional motion results are presented. For the months of May 1988 and October–November 1987, we find rotation coefficients A = 2.894 ± 0.011, B = - 0.428 ± 0.070, and C = -0.370 ± 0.077 in rad s–1 from the expansion = A + B sin2 + C sin4, where is the latitude. The differential rotation curve for this interval is essentially flat within 20 deg of the equator in these intervals. For the same intervals we find a poleward meridional motion a = 16.0 ± 2.8 m sec -1 from the relation v = a sin, where v is the line-of-sight velocity.Operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 相似文献
11.
The occurrence at a heliocentric distance of 1 AU of alpha particle streaming velocities larger than proton streaming velocities,v
/v
p
>1 (Ogilvie, 1975) is investigated on the basis of the theory suggesting the existence in the solar wind of an accelerating force acting preferentially on the alpha particles.Accurate solution of the three-fluid model equations for the quiet solar wind indicates that anecessary andsufficient condition for (v
/v
p
)1 AU>1 is the presence of a relativelyweak accelerating forceacting in a limited region in the vicinity of 1 AU. If the force is effectiveonly at small heliocentric distances, the alpha particle streaming velocity excess vanishes at distances less than 1 AU, because of the (equalization) action of the dynamical friction force. 相似文献
12.
The interaction of rotation and turbulent convection is assumed to give rise to an inhomogeneous, but isotropic, latitude dependent turbulent energy transport, which is described by a convective conduction coefficient
c which varies with latitude. Energy balance in the convective zone is then possible only with a slow meridian circulation in the outer convective zone of the sun. The angular momentum transported by this circulation is balanced in a steady state by turbulent viscous transport down an angular velocity gradient. A detailed model is constructed allowing for the transition from convective transport to radiative transport at the boundaries of the convective zone, by using a perturbation analysis in which the latitude variation of
c is small. The solution for a thin compressible shell gives equatorial acceleration and a hotter equator than pole, assuming that the convection is preferentially stabilised at the equator. For agreement with the sun's equatorial acceleration the model predicts an equatorial temperature excess of 70 K and a surface meridional velocity of 350 cm/sec from pole to equator. 相似文献
13.
We report quantitative analysis of the radial gradient of solar angular velocity at depths down to about 15 Mm below the solar surface for latitudes up to 75° using the Michelson Doppler Imager (MDI) observations of surface gravity waves (fmodes) from the Solar and Heliospheric Observatory (SOHO). A negative outward gradient of around –400 nHz/R
, equivalent to a logarithmic gradient of the rotation frequency with respect to radius which is very close to –1, is found to be remarkably constant between the equator and 30° latitude. Above 30° it decreases in absolute magnitude to a very small value at around 50°. At higher latitudes the gradient may reverse its sign: if so, this reversal takes place in a thin layer extending only 5 Mm beneath the visible surface, as evidenced by the most superficial modes (with degrees l>250). The signature of the torsional oscillations is seen in this layer, but no other significant temporal variations of the gradient and value of the rotation rate there are found. 相似文献
14.
Yu. V. Vandakurov 《Astronomy Letters》2001,27(9):596-607
In view of the recently discovered time variations in rotation velocity within the solar differentially rotating tachocline (Howe et al. 2000), we study conditions for the equilibrium and excitation of motions in nonrigidly rotating magnetized layers of the radiative zones located near the boundaries of the convection zone. The emphasis is on the possible relationship between quasi-periodic tachocline pulsations and the generation of a nonaxisymmetric magnetic field in the convection zone. This field generation is studied under the assumption that it results from a reduction in the expenditure of energy on convective heat transport. The (antisymmetric about the equator) field is shown to increase in strength if there are both a radial gradient in angular velocity and steady-state axisymmetric meridional circulation of matter. The sense of circulation is assumed to change (causing the sign of the generated field to change) after the maximum permissible field strength is reached. This is apparently attributable to the excitation of the corresponding turbulent viscosity of the medium. It is also important that the cyclic field variations under discussion are accompanied by variations in solar-type dipole magnetic field. 相似文献
15.
A rocket-borne coronagraph utilizing external occulting disks was used to photograph the solar corona from 3 to 9 R
s at 1931 UT on 7 March, 1970. Comparison of the rocket and ground-based observations shows a one-to-one correspondence between major streamers from the inner to the outer corona. In particular streamers over the poles are clearly visible against the background corona from 3 to 8 R
s. These rocket data had a scattered light level of 1.2 × 10–10
B
s. The derived quiet equatorial and polar K + F corona was within 10% of the absolute brightness of standard coronal models and displayed identical radial gradients to those models. The photometric profiles of the NE limb streamer were analyzed assuming a model in which the core density follows a Gaussian distribution in directions perpendicular to the radius vector. This streamer was assumed to be rooted on the visible disk at 55 to 60° from the plane-of-the-sky as based on K-coronameter and XUV data. An uncertainty of as much as a factor of three still remains for the value of the axis density owing to uncertainty in the line-of-sight dimension of the streamer. 相似文献
16.
Recently Mayr et al. (1980) have suggested that the superrotation of planetary atmospheres could, in principle, be understood as a pirouette. Equatorial heating is pumping atmospheric material toward the poles, and with a concomitant reduction in moment of inertia, the atmosphere has the tendency of spinning up. On the Sun, the core is assumed to be rotating with a period of about 12 days (Dicke, 1976; Knight et al., 1979) while the overlaying mantle convection zone has a solid body component of about 27 days. We propose here that this phenomenon could simply be understood as a reverse pirouette. Our model is similar to the models put forth by Kippenhahn (1963), Weiss (1965), Durney (1968), Busse (1970), Yoshimura (1972), Gilman (1974), and Gierasch (1974). Whereas the models listed provided solutions of valid equations and computer analyses, they lack a simple physical picture to explain the phenomenon. In our case, we have the solar oblateness conventionally providing added heat input at the poles. The result is the large scale transport of material toward the equator giving rise to subrotation. The model thus facilitates an understanding of the formation of a slowly rotating convection zone above the more rapidly rotating core. The latitudinal photospheric differential rotation is interpreted as a second order effect associated with horizontal momentum transport. The recent observations of zonal winds drifting equatorward with a 22-year period (Howard and LaBonte, 1980) may be related by this model as a third order effect from a similar periodicity in differential solar heating (pole to equator). 相似文献
17.
In this paper temperature enhanced -decay at high stellar temperatures is investigated in conjunction withs-process nucleosynthesis. The temperature dependence of -decay is the result of more energetic, hence faster, decay from thermally excited nuclear states. A formula for the effective halflife is derived as a function of the atomic number and weight, temperature, and the -decayQ-value of the isotope. The effect of such enhanced -decay upons-process abundances is discussed, and information abouts-process neutron flux intensities is deduced based on the calculated -decay halflives of the isotopes Nd 144 and Sm 150. The neutron flux-temperature relationships are compared to specific constant temperature carbon-burning models of massive stars which are considered to be possible sources of solar systems-process abundances. Finally, information regarding the time betweens-process termination and final interstellar injection ofs-process material is derived using the decay calculations. 相似文献
18.
The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean‐field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar‐type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increases monotonically with depth at all latitudes throughout the whole convection zone. In the lower part of the convection zone the horizontal shear vanishes and there is a strong radial gradient. The surface meridional flow has maximum speed of 170 m/s and is directed towards the equator at high and towards the poles at low latitudes. Turbulent magnetic diffusivity is of the order 1015–1016 cm2/s. The conditions on Arcturus are not favorable for a circulation‐dominated dynamo (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
We analyzed 689 high-resolution magnetograms taken daily with the NSO Vacuum Telescope on Kitt Peak from 1975 to 1991. Motions in longitude on the solar surface are determined by a one-dimensional crosscorrelation analysis of consecutive day pairs. The main sidereal rotation rate of small magnetic features is best fit by = 2.913(±0.004) – 0.405(±0.027) sin2
– 0.422(±0.030) sin4
, in µrad s–1, where is the latitude. Small features and the large-scale field pattern show the same general cycle dependence; both show a torsional oscillation pattern. Alternating bands of faster and slower rotation travel from higher latitudes toward the equator during the solar cycle in such a way that the faster bands reach the equator at cycle minimum. For the magnetic field pattern, the slower bands coincide with larger widths of the crosscorrelations (corresponding to larger features) and also with zones of enhanced magnetic flux. Active regions thus rotate slower than small magnetic features. This magnetic torsional oscillation resembles the pattern derived from Doppler measurements, but its velocities are larger by a factor of more than 1.5, it lies closer to the equator, and it leads the Doppler pattern by about two years. These differences could be due to different depths at which the different torsional oscillation indicators are rooted.Operated by the Association of Universities for Research in Astronomy Inc. under cooperative agreement with the National Science Foundation. 相似文献
20.
We study the possibility that large flux differences between the poles and the equator at the bottom of the solar convective zone are compatible with the small differences observed at the surface. The consequences of increasing the depth of the convective zone due to overshooting are explored.A Boussinesq model is used for the convective zone and we assume that the interaction of the global convection with rotation is modelled through a convective flux coefficient whose perturbed part is proportional to the local Taylor number. The numerical integration of the equations of motion and energy shows that coexistence between large pole-equator flux differences at the bottom and small ones at the surface is possible if the solar convective zone extends to a depth of 0.4R
. The angular velocity distribution inside the convective zone is in agreement with the -dynamo theories of the solar cycle. 相似文献