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1.
We present the 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 meridional 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 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'.  相似文献   

2.
The first 3-D non-linear hydrodynamical simulation of the inner convective envelope of a rotating low mass red giant star is presented. This simulation, computed with the ASH code, aims at understanding the redistribution of angular momentum and heat in extended convection zones. The convection patterns achieved in the simulation consist of few broad and warm upflows surrounded by a network of cool downflows. This asymmetry between up and downflows leads to a strong downward kinetic energy flux, that must be compensated by an overluminous enthalpy flux in order to carry outward the total luminosity of the star. The influence of rotation on turbulent convection results in the establishment of largescale mean flows: a strong radial differential rotation and a single cell poleward meridional circulation per hemisphere. A detailed analysis of angular momentum redistribution reveals that the meridional circulation transports angular momentum outward in the radial direction and poleward in the latitudinal direction, with the Reynolds stresses acting in the opposite direction. This simulation indicates that the classical hypothesis of mixing length theory and solid-body rotation in the envelope of red giants assumed in 1-D stellar evolution models are unlikely to be realized and thus should be reconsidered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
Laurent Gizon 《Solar physics》2004,224(1-2):217-228
Flows in the upper convection zone are measured by helioseismology on a wide variety of scales. These include differential rotation and meridional circulation, local flows around complexes of magnetic activity and sunspots, and convective flows. The temporal evolution of flows through cycle 23 reveals connections between mass motions in the solar interior and the large-scale characteristics of the magnetic cycle. Here I summarize the latest observations and their implications. Observations from local helioseismology suggest that subsurface flows around active regions introduce a solar-cycle variation in the meridional circulation.  相似文献   

4.
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   

5.
In the solar convection zone, rotation couples with intensely turbulent convection to build global-scale flows of differential rotation and meridional circulation. Our sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the patterns of convection in such stars and the global-scale flows which are self-consistently established. The convection in these systems is richly time dependent and in our most rapidly rotating suns a striking pattern of spatially localized convection emerges. Convection near the equator in these systems is dominated by one or two patches of locally enhanced convection, with nearly quiescent streaming flow in between at the highest rotation rates. These active nests of convection maintain a strong differential rotation despite their small size. The structure of differential rotation is similar in all of our more rapidly rotating suns, with fast equators and slower poles. We find that the total shear in differential rotation, as measured by latitudinal angular velocity contrast, ΔΩ, increases with more rapid rotation while the relative shear, ΔΩ/Ω, decreases. In contrast, at more rapid rotation the meridional circulations decrease in both energy and peak velocities and break into multiple cells of circulation in both radius and latitude. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

6.
We have performed 3-D numerical simulations of compressible convection under the influence of rotation and magnetic fields in spherical shells. They aim at understanding the subtle coupling between convection, rotation and magnetic fields in the solar convection zone. We show that as the magnetic Reynolds number is increased in the simulations, the magnetic energy saturates via nonlinear dynamo action, to a value smaller but comparable to the kinetic energy contained in the shell, leading to increasingly strong Maxwell stresses that tend to weaken the differential rotation driven by the convection. These simulations also indicate that the mean toroidal and poloidal magnetic fields are small compared to their fluctuating counterparts, most of the magnetic energy being contained in the non-axisymmetric fields. The intermittent nature of the magnetic fields generated by such a turbulent convective dynamo confirms that in the Sun the large-scale ordered dynamo responsible for the 22-year cycle of activity can hardly be located in the solar convective envelope.  相似文献   

7.
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   

8.
Sunspot position data obtained from Kanzelhöhe Observatory for Solar and Environmental Research (KSO) sunspot drawings and white light images in the period 1964 to 2016 were used to calculate the rotational and meridional velocities of the solar plasma. Velocities were calculated from daily shifts of sunspot groups and an iterative process of calculation of the differential rotation profiles was used to discard outliers. We found a differential rotation profile and meridional motions in agreement with previous studies using sunspots as tracers and conclude that the quality of the KSO data is appropriate for analysis of solar velocity patterns. By analyzing the correlation and covariance of meridional velocities and rotation rate residuals we found that the angular momentum is transported towards the solar equator. The magnitude and latitudinal dependence of the horizontal component of the Reynolds stress tensor calculated is sufficient to maintain the observed solar differential rotation profile. Therefore, our results confirm that the Reynolds stress is the dominant mechanism responsible for transport of angular momentum towards the solar equator.  相似文献   

9.
Wittmann  A. 《Solar physics》1974,34(1):11-14
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   

10.
The Debrecen Photoheliographic Data catalogue is a continuation of the Greenwich Photoheliographic Results providing daily positions of sunspots and sunspot groups. We analyse the data for sunspot groups focussing on meridional motions and transfer of angular momentum towards the solar equator. Velocities are calculated with a daily shift method including an automatic iterative process of removing the outliers. Apart from the standard differential rotation profile, we find meridional motion directed towards the zone of solar activity. The difference in measured meridional flow in comparison to Doppler measurements and some other tracer measurements is interpreted as a consequence of different flow patterns inside and outside of active regions. We also find a statistically significant dependence of meridional motion on rotation velocity residuals confirming the transfer of angular momentum towards the equator. Analysis of horizontal Reynolds stress reveals that the transfer of angular momentum is stronger with increasing latitude up to about \(40^{\circ}\), where there is a possible maximum in absolute value.  相似文献   

11.
An axisymmetric model for the Sun's differential rotation based upon a mechanism for angular momentum transport by compressible convection is developed. Convective heat transport is also considered. The model is simplified by the neglect of meridional circulation and radiative heat transport but is otherwise a self-consistent one because no adjustable parameters are used and the effective transport coefficients are expressed explicitly in terms of superadiabaticity of stratification rather than assigned externally. The model predictions agree satisfactorily with the observed rotation of the photosphere and with helioseismology data. The dependence of the rotation law, produced by the model, on rotation rate of a Sun-like star is discussed.  相似文献   

12.
The law of rotation as well as the corresponding meridional circulations in the hydrogen convection zone (HCZ) are investigated by solving numerically the time independent Navier-Stokes equations. The HCZ is assumed to be a spherical layer of fluid with constant density and viscosity. It is assumed further that the viscosity is caused by unisotropic turbulent motions.The results show differential rotation together with circulations. The detailed behaviour depends on a parameters characterizing the nonisotropic friction and on the kinematic viscosityv. If the friction is larger in radial direction than in lateral directions (0 s < 1) the poles rotate faster than the equator and the circulation rises at the equator and falls at the poles; if friction is smaller in radial direction (s > 1) the equator rotates faster and the sense of the circulation is reversed. The differential rotation observed at the solar surface is obtained for the values = 1.2.For small values ofv the angular velocity is constant on cylindrical surfaces, for large values ofv it is constant on spherical surfaces. The solar law of rotation turns out to be very close to the first case.Based on the author's Thesis in Göttingen.  相似文献   

13.
We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

14.
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:
  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.
  2. A flux difference between pole and equator at the surface of about 5 percent, the poles being hotter.
  3. An angular velocity increasing inwards.
  4. 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.
  相似文献   

15.
We examine the effects of rotation about a vertical axis on thermal convection with a simple model in which an inviscid, incompressible fluid of zero thermal conductivity and electrical resistivity is contained in a thin annulus of rectangular cross-section. The initial steady state assumed is one of no motion relative to the rotating frame with constant (unstable) vertical temperature gradient and uniform toroidal magnetic field. Small periodic disturbances are then introduced and the linearized perturbation equations solved. We also determine the second-order mean circulations and magnetic fields that are forced by non-zero Reynolds and thermal stresses and magnetic field transports.The solutions have several properties which are relevant to large-scale solar phenomena if giant long-lived convection cells exist on the sun. In particular, the convective cells are tilted in latitude in the same sense as bipolar magnetic regions, and induce vertical magnetic fields with the same tilt. They transport momentum across latitude circles through Reynolds stresses and induced meridional circulations thus setting up a differential rotation. Cells which grow slowly compared to the rotation rate and have comparable dimensions in latitude and longitude transport momentum toward the equator. The cells also form a poloidal magnetic field from initial toroidal field, in a manner similar to that put forth by Parker.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

16.
The evolution of a rotating star with a mass of 16M ⊙ at the hydrogen burning phase is considered together with the hydrodynamic processes of angular momentum transport in its interior. Shear turbulence is shown to limit the amplitude of the latitudinal variations in mean molecular weight on a surface of constant pressure in a layer with variable chemical composition. The resulting nonuniformity in the mean molecular weight distribution and the turbulent energy transport along the surface of constant pressure reduce the absolute value of the meridional circulation velocity. Nevertheless, meridional circulation remains the main mechanism of angular momentum transport in the radial direction in a layer with variable chemical composition. The intensity of the processes of angular momentum transport by meridional circulation and shear turbulence is determined by the angular momentum of the star. At a fairly high angular momentum, more specifically, at J = 3.69 × 1052 g cm2 s?1, the star during the second half of the hydrogen-burning phase in its convective core has characteristics typical of classical early Be stars.  相似文献   

17.
Hathaway  David H. 《Solar physics》1988,117(2):329-341
A method is described for constructing artificial data that realistically simulate photospheric velocity fields. The velocity fields include rotation, differential rotation, meridional circulation, giant cell convection, supergranulation, convective limb shift, p-mode oscillations, and observer motion. Data constructed by this method can be used for testing algorithms designed to extract and analyze these velocity fields in real Doppler velocity data.  相似文献   

18.
Self‐consistent convective dynamo simulations in wedge‐shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large‐scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
Miesch  Mark S. 《Solar physics》2000,192(1-2):59-89
In recent years, helioseismology has provided an unprecedented look at the dynamics of the solar interior. These new insights have been accompanied by tremendous advances in high-performance computing technology, prompting increasingly sophisticated and realistic numerical models of solar convection. Among the most important helioseismic constraints on global-scale convection models is the mean differential rotation profile of the solar envelope, which is established by convection under the influence of rotation. The highly turbulent nature of solar convection makes this rotational influence difficult to determine and model. I will begin this review by discussing the solar rotation profile inferred from helioseismic measurements and various theoretical and numerical approaches to account for it. Computational constraints limited early numerical models to relatively laminar flow regimes but more recent investigations have begun to explore the distinct nature of turbulent convection. After a brief overview of empirical and numerical results on the related Rayleigh-Bernard system, I will outline the current state of numerical modeling of turbulent convection in rotating, stratified fluids, first in Cartesian and then in spherical geometries. The emphasis throughout will be on how rotation influences the structure, evolution, and transport processes of turbulent convection and what type of differential rotation can result.  相似文献   

20.
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   

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