Magnetic flux separation in photospheric convection

Three-dimensional non-linear magnetoconvection in a strongly stratified compressible layer exhibits different patterns as the strength of the imposed magnetic field is reduced. There is a transition from a magnetically dominated regime, with small-scale convection in slender hexagonal cells, to a convectively dominated regime, with clusters of broad rising plumes that confine the magnetic flux to narrow lanes where fields are locally intense. Both patterns can coexist for intermediate field strengths, giving rise to flux separation: clumps of vigorously convecting plumes, from which magnetic flux has been excluded, are segregated from regions with strong fields and small-scale convection. A systematic numerical investigation of these different states shows that flux separation can occur over a significant parameter range and that there is also hysteresis. The results are related to the fine structure of magnetic fields in sunspots and in the quiet Sun.     

Magnetic field transfer by two-dimensional convection and solar ‘semi-dynamo’

A comparison of the equations for the magnetic field transfer and for the heat transfer by two-dimensional turbulent convection of a conducting compressible medium shows the magnetic field to be transported as a scalar admixture provided it is parallel to the convective rolls. At high magnetic Reynolds numbers the field strength in a convective zone varies proportionally to the density of the medium.A study of the distribution and amplification of the poloidal field in the two-dimensional convection zone of the Sun lying under the supergranulation, together with the processes of field pumping and amplification in other zones, reveals the importance of considering generation mechanisms of thesemi-dynamo type where the amplifying field is excited independently by weak e.m.f.'s of non-electric origin with no feedback which would otherwise produce MHD self-excitation of the field.An illustrative calculation of the solar poloidal field maintained by a weak Coriolis e.m.f. acting in a thin external layer of the convective envelope yields for the general near-polar field, if one somehow takes into account (1) field pumping by three-dimensional supergranulation, (2) field transfer and amplification by two-dimensional convection, and (3) ohmic diffusion of the field into a stable core, a value of the order of 10^–1 gauss.     

Solar convection

The hydrodynamics of solar convection is reviewed. In particular, a discussion is given of convection on the scale of granulation; i.e., the energy carrying convection patterns in the solar surface layers, and its penetration into the stable layers of the solar photosphere. Convection on global and intermediate scales, and interaction with rotation and magnetic fields is discussed briefly.     

Probing solar convection

In the solar convection zone, acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov's technique. Particular care is taken to include diffraction effects, which are important, especially for high-degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p-mode eigenfrequencies. The contribution of scattering to the linewidths is estimated and the sensitivity of the results to the assumed spectrum of the turbulence is studied. Finally, the theoretical predictions are compared with recently measured linewidths of high-degree modes.     

On efficiency of convection of Öpik's cellular convection theory

The physical meaning of the convection efficiency parameter of Öpik's theory is clarified by relating it to that of the mixing-length theory. A compact comparison of both theories is presented to explain the earlier findings of Gough and Weiss (1976), that Öpik's theory becomes indistinguishable from the mixing-length theory when the value of Öpik's cell depth is taken as being equal to 2.44 times the local pressure scale height for the solar convective envelope.     

Turbulent compressible convection with rotation–penetration below a convection zone

We examine the behaviour of penetrative turbulent compressible convection under the influence of rotation by means of three dimensional numerical simulations. We estimate the extent of penetration below a stellar-type rotating convection zone in an f-plane configuration. Several models have been computed with a stable-unstable-stable configuration by varying the rotation rate (Ω), the inclination of the rotation vector and the stability of the lower stable layer. The spatial and temporal average of kinetic energy flux (F_k) is computed for several turnover times after the fluid has thermally relaxed and is used to estimate the amount of penetration below the convectively unstable layer. Our numerical experiments show that with the increase in rotational velocity, the downward penetration decreases. A similar behaviour is observed when the stability of the lower stable layer is increased in a rotating configuration. Furthermore, the relative stability parameter S shows an S ^−1/4 dependence on the penetration distance implying the existence of a thermal adjustment region in the lower stable layer rather than a nearly adiabatic penetration region.     

Seismic study of solar convection and overshooting: results of nonlocal convection

Local mixing-length theory is incapable of describing nonlocal phenomena in stellar convection, such as overshooting. Therefore standard solar models constructed with local mixing-length theory significantly deviate from the Sun at the boundaries of the convection zone, where convection becomes less efficient and nonlocal effects are important. The differences between observed and computed frequencies mainly come from the region near the surface, while the localized difference in sound speed is just below the convective envelope. We compute a solar envelope model using Xiong’s nonlocal convection theory, and carry out helioseismic analysis. The nonlocal model has a smooth transition at the base of the convection zone, as revealed by helioseismology. It reproduces solar frequencies more accurately, and reduces the localized difference in sound speed between the Sun and standard solar models.     

On large-scale solar convection

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.     

Thermal convection in the porous methane-soaked regolith in Titan: Finite amplitude convection

Titan is the only body, beside the Earth, where liquid is present on the surface. This paper is aimed to show the properties of possible convection in a porous regolith on Titan. In our previous work (Czechowski, L., Kossacki, K.J. [2009]. Icarus 202, 599–607) we showed, that the Rayleigh number Ra can exceed its critical value Ra_c. Hence, the convective motion of liquid filling pores in the regolith is likely for Titan relevant parameters. In the present work we investigate the properties of finite amplitude convection, i.e. for Ra > Ra_cr. We study the basic properties of the steady state solution, the Nusselt number, the density of the heat flow and the average temperatures. Evolution of the convection is also considered. We conclude that any reasonable thermal model of Titan’s regolith should take into account the possibility of the considered convection. We discuss also possibility of identification of this convection (or its consequences in the form of evaporates) by the Cassini and possible future spacecrafts.     

Solar magnetic fields and convection

Solar meridional drift motions are vitally important in connection with the origin of magnetic fields, the source of differential rotation, and perhaps convection. A large body of observational evidence is collated with the following conclusions. (i) Sunspot motions reveal latitudinal drifts (Figures 2 and 3) of a few metres per second which vary with latitude and have a strong 11-yr periodicity. There may also be a 22-yr component polewards during even cycles and equatorwards during odd. (ii) Various other tracers, all basically magnetic structures, show the 11-yr drifts at mid- and high latitudes up to the polar caps, motion being polewards during the three years starting just before minimum activity (Figure 4). (iii) The earlier evidence for giant cells or Rossby-type waves is shown to be merely misinterpretation of the hydromagnetic motions of tracers. Evidence against such giant eddies is found in the great stability of other tracer structures. (iv) From the various tracer motions a four cell axisymmetric meridional drift system is determined (Figure 5 (b)) with an 11-yr period of oscillation and amplitude a few metres per second. (v) These meridional oscillations must be a basic component of the activity cycle. They add to the difficulties of the dynamo theory, but may explain the emergence of stitches of flux ropes to form relatively small bipolar magnetic regions. (vi) The two cells also throw light on thetwo sunspot zones in each hemisphere, discussed earlier by Becker and by Antalová and Gnevyshev.     

Solar magnetic fields and convection

The flux-rope-fibre model of solar magnetic fields is developed further to cover post-spot evolution of the fields, faculae, and the influence of magnetic fields on some convective motions. (i) Unipolar magnetic regions of a strongly dominant polarity are explained, as are some fields outside the network, and some tiny reversed polarity fields. (ii) The migration of magnetic regions is explained: the following regions to the poles where most of the flux just vanishes and the preceding towards the equator. (iii) The model explains the rotation of the gross pattern of background fields with a period of 27 days. It explains the puzzling features of active longitudes and of magnetic longitudes extending across the equator. (iv) The magnetic model provides a framework for the various chromospheric fine structures, the rosettes, bushes, double chains, mottles and spicules. It provides qualitative models of these features and points the way to a very complicated quantitative model of the network. (v) Several new convective patterns are described and explained in terms of magnetic stresses. The first is the moat around sunspots, which replaces the supergranule motions there. The second is the long-lived (4–7 days) supergranule cell enclosed by strong fields. The third is a small-scale () convective motion, and the fourth is aligned or long granules, both caused by small-scale magnetic fields. (vi) Photospheric line faculae and photospheric continuum faculae are different phenomena. The former, like the chromospheric faculae, are caused by Alfvén-wave heating. The latter are caused by a new small-scale convective motion. (vii) A model of the 3-min oscillation is described.     

Solar magnetic fields and convection

The traditional model of solar magnetic fields is based on convection which dominates generally weak, diffuse fields and so tends to create increasingly tangled fields. Surplus fields must be eliminated by merging of opposite polarities; for example a solar dynamo of period≈10 yr requires fields to be reduced to a scale of<100 km or diffusivity to be increased by a factor of≈10⁷ over molecular diffusivity. It is now shown that the true requirements of any diffuse-field theory are far more stringent, and that surplus fields must be eliminated within a single eddy period of 1 day (10 min) for the supergranules (granules). The reason is that during that period fresh fields are created with flux and energy comparable with those of the old fields. The numerical models of Weiss and Moss are used to confirm this result which is fatal to all diffuse-field theories. The basic error in these theories is found in the assumption that because heat and other passive properties of a fluid diffuse much faster in the presence of turbulence, passive magnetic fields should do likewise. The error is that the heat content of an eddy is not increased by the motion while the magnetic flux and energy are increased rapidly. It is shown that the observed concentrations of surface fields into strengths of?100 G cannot be accounted for by observed surface motions. Nor are they accounted for by the numerical models of turbulence of Weiss or Moss whatever values of the magnetic Reynolds number are assumed. A detailed comparison is made between both small-scale and large-scale surface magnetic features and the predictions of the diffuse-field theory. The differences appear irreconcilable and the features only explicable in terms of the twisted flux-rope model.     

Supersonic convection in stellar interiors

According to the result of the numerical simulation on stellar convective envelopes by the traditional mixing length theory, supersonic convection would occur on the top of the convective regions of the yellow-and-red giants and supergiants. This, however, is not self-consistent with the local convection theory itself. This paper is devoted to analyze in details the origin of supersonic convection, and at the same time to present a plot of the supersonic convection region on the H-R diagram based on the evolutionary track of population I stars. The main results of this paper are as follows: in the process of evolution, (1) no supersonic convection occurs in low-mass stars; (2) for intermediate-mass stars, because of the ionization of hydrogen, the supersonic convection occurs chiefly in the region of 3.6< lgT_e <4.0, tilting from the lower left to the upper right on the H-R diagram and extending to the region of red giants for relatively massive stars; (3) for massive stars, the supersonic convection occurs after they deviate from ZAMS, the greater the stellar mass is, the earlier the supersonic convection emerges. For blue supergiants, the supersonic convection occurs at the absorbtion peak (lg T ∼5.3) of Fe and in the secondary ionization region of helium, but for the red- and yellow-giants and supergiants, it occurs in the ionization region of hydrogen.     

Solar magnetic fields and convection

The solar magnetic fields observed in active regions and their residues are thought to be parts of toroidal field systems renewed every 11-yr cycle from a poloidal field. The latter may be either a reversing (dynamo) field or a non-reversing, primordial field. The latter view was held for some 70 yr, but the apparent reversals of the polar-cap fields in 1957–8 and the development of dynamo theory brought wide acceptance of the former. Here we consider evidence for and against each model, with these conclusions. (i) Several errors combine so that the non-spot measurements of gross magnetic fluxes are too low by factors of 10 or more. A permanent field of 2 G or more might remain unobserved. (ii) Measurements of average magnetic field strength are subject to various large errors. In particular, the reported reversals of the polar-cap fields are better explained in terms of tilts of toroidal field residues. (iii) Observations of new-cycle magnetic fields among old-cycle fields, of the gradual fading away of large unipolar regions, and the ubiquitous jumble of very small magnetic loop structures appear explicable only in terms of a primordial field. (iv) More positive evidence of a primordial field is found in the extreme order, symmetry and long-term stability of the polar cap streamers or rays. During one eclipse (1954) the primordial field was seen in the absence of all toroidal field residues. (v) A form of reversal of the interplanetary magnetic field is re-interpreted and shown to be consistent with a primordial, but not a dynamo, field. (vi) A test for a primordial field is that the fields below coronal holes should tend to be positive (outwards) in the northern hemisphere and negative in the southern hemisphere. (vii) Further evidence may be available by studying various plasma structures below coronal holes. An urgent requirement is a study of fibrils, faculae, macrospicules and rays in these regions.     

Solar magnetic fields and convection

Recent developments in solar dynamo and other theories of magnetic fields and convection are discussed and extended. A basic requirement of these theories, that surplus fields are eliminated by turbulent or eddy diffusion, is shown to be invalid. A second basic requirement, that strong surface fields are created by granule or supergranule motions, is shown to be improbable. Parker's new thin-filament dynamo, based on the Petschek mechanism, is shown to provide the alternative possibilities: either the magnetic fields halt all convection or a steady state is reached in which the fields are a tangle of long, thin filaments. From the above and other considerations it is concluded that the dynamo and related diffuse-field theories are unacceptable, that solar magnetic fields are not dominated by convection, and that all the fields emerge as strong, concentrated fields (flux ropes) which were wound and twisted from a permanent, primordial field. The discussion may, incidentally, provide the physical elements of a deductive theory of hydromagnetic convection.     

On convection in the sun

Convective motions driven by a superadiabatic temperature gradient in a viscous thermally conductive medium are considered. Approximate linearized equations governing the perturbation are derived under the following conditions: (i) The ratio of the excess temperature gradient over the adiabatic gradient is small compared with the gradient itself, (ii) The perturbation is of low-frequency type, (iii) The rotation is slow. Only the convective mode is described by these equations (as in the Boussinesq approximation), and the equations are valid for compressible configurations with any ratio between the scale heights of the equilibrium and perturbed quantities. Results of a numerical calculation of unstable perturbations for configurations with a large density stratification are given. They show that under conditions appropriate for the solar convection zone an extremely strong instability is expected to occur if the mixing length is assumed to be equal to 1.5 times the pressure scale height. The horizontal scale of the instability is intermediate between those of granulation and supergranulation. The larger the mixing length, the smaller the growth rate of the instability, and the larger its horizontal scale. Therefore it seems possible to adjust the mixing length to obtain the characteristics corresponding to those of the solar supergranulation. The possible origin of the granulation as an instability in a subsurface zone, where a local increase in the density scale height takes place, is also discussed. To achieve agreement with observations, it seems necessary to assume that the ratio of the mixing length to pressure scale height is an increasing function of the pressure.     

A large-eddy simulation of turbulent compressible convection: differential rotation in the solar convection zone

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'.     

A generalized time-dependent local convection theory

The time-dependent convection theory given in [1] is generalized to include non-radial oscillations. Under some reasonable assumptions, dynamic equations are derived of the auto-correlation and cross-correlation functions of the velocity and temperature fluctuations. Steady and pulsating components are separated and solved for. Our steady component agrees with Vitense's formulae. The pulsating component contains a phase-lag, due to the inertia of the convective motion.     

Implications of a steady-state magnetospheric convection

Fundamental to the development of many magnetospheric theories is the assumption of a steady-state magnetospheric convection. It is shown for the first time that this basic assumption is implicitly related to the source of magnetospheric plasma. The existence of a steady-state electric field is consistent with plasma entry into the magnetosphere from the North—South direction. If plasma entry is through the flanks of the magnetosphere, the large-scale magnetospheric electric field is intrinsically time-dependent. Thus, magnetospheric theories with the underlying assumption that the large-scale electric field is derivable from a scalar potential cannot deal with such a situation. Therefore, the origin of magnetospheric plasma and the time-variability of magnetospheric convection are directly related.     

Jovian meteorology: Large-scale moist convection

The suggestion that latent heat of water controls Jovian meteorology is reviewed and predictions are made for the other outer planets. The observed slow variation and two-dimensional character of motions at cloud top level is explained. It depends on (a) the thermal structure between water cloud level and the level of emission to space being closely adiabatic, and (b) the large static stability of the emission layer.