The dynamics of jovian white ovals from formation to merger

In early 1998 two of the three, long-lived anticyclonic, jovian white ovals merged. In 2000 the two remaining white ovals merged into one. Here we examine that behavior, as well as the dynamics of three earlier epochs: the Formation Epoch (1939-1941), during which a nearly axisymmetric band broke apart to form the vortices; the Kármán Vortex Street Epoch (1941-1994), during which the white ovals made up the southern half of two rows of vortices, and their locations oscillated in longitude such that the white ovals often closely approached each other but did not merge; and the Pre-merger Epoch (1994-1997), during which the three white ovals traveled together with intervening cyclones from the northern row of the Kármán vortex street in a closely spaced group with little longitudinal oscillation. We use a quasi-geostrophic model and large-scale numerical simulation to explain the dynamics. Our models and simulations are consistent with the observations, but none of the observed behavior is even qualitatively possible without assuming that there are long-lived, coherent cyclones longitudinally interspersed with the white ovals. Without them, the white ovals approach each other and merge on a fast, advective timescale (4 months). A necessary ingredient that allows the vortices to travel together in a small packet without spreading apart is that the strong, eastward-flowing jetstream south of the white ovals is coincident with a sharp gradient in background potential vorticity. The jet forms a Rossby wave and a trough of the wave traps the white ovals. In our simulations, the three white ovals were trapped before they merged. Without being trapped, the amount of energy needed to perturb two white ovals so that they merge exceeds the atmosphere’s turbulent energy (which corresponds to velocities of ∼1 m s⁻¹) by a factor of ∼100. The mergers of the white ovals BC and DE were not observed directly, so there is ambiguity in labeling the surviving vortices and identifying which vortices might have exchanged locations. The simulation and modeling make the identifications clear. They also predict the fate of the surviving white oval and of the other prominent jovian vortex chains.     

Measures of Jupiter photographs—1974/1975 apparition

The 1974/1975 Jupiter apparition is described. Photographic images have been measured and zonal velocities are given for all spots observed on four or more dates. Global and localized zonal flow patterns are graphically presented. Methane absorption band imagery at 890 nm indicates that white ovals and red spots are high in altitude, and blue features are cloud-free areas. The motions of blue features are complex and unlike the motions of other features. Interactions or associations between spots at five adjacent atmospheric currents have been observed. Zonal motion within an equatorial plume has been observed. Evidence is presented for a probable source of red spots in the North Tropical Zone.     

Persistent rings in and around Jupiter’s anticyclones – Observations and theory

We present observations and theoretical calculations to derive the vertical structure of and secondary circulation in jovian vortices, a necessary piece of information to ultimately explain the red color in the annular ring inside Jupiter’s Oval BA. The observations were taken with the near-infrared detector NIRC2 coupled to the adaptive optics system on the 10-m W.M. Keck telescope (UT 21 July 2006; UT 11 May 2008) and with the Hubble Space Telescope at visible wavelengths (UT 24 and 25 April 2006 using ACS; UT 9 and 10 May 2008 using WFPC2). The spatial resolution in the near-IR (∼0.1–0.15″ at 1–5 μm) is comparable to that obtained at UV–visible wavelengths (∼0.05–0.1″ at 250–890 nm). At 5 μm we are sensitive to Jupiter’s thermal emission, whereas at shorter wavelengths we view the planet in reflected sunlight. These datasets are complementary, as images at 0.25–1.8 μm provide information on the clouds/hazes in the troposphere–stratosphere, while the 5-μm emission maps yield information on deeper layers in the atmosphere, in regions without clouds. At the latter wavelength numerous tiny ovals can be discerned at latitudes between ∼45°S and 60°S, which show up as rings with diameters ?1000 km surrounding small ovals visible in HST data. Several white ovals at 41°S, as well as a new red oval that was discovered to the west of the GRS, also reveal 5-μm bright rings around their peripheries, which coincide with dark/blue rings at visible wavelengths. Typical brightness temperatures in these 5-μm bright rings are 225–250 K, indicative of regions that are cloud-free down to at least the ∼4 bar level, and perhaps down to 5–7 bar, i.e., well within the water cloud.Radiative transfer modeling of the 1–2 μm observations indicates that all ovals, i.e., including the Great Red Spot (GRS), Red Oval BA, and the white ovals at 41°S, are overall very similar in vertical structure. The main distinction between the ovals is caused by variations in the particle densities in the tropospheric–stratospheric hazes (2–650 mbar). These are 5–8 times higher above the red ovals than above the white ones at 41°S. The combination of the 5-μm rings and the vertical structure derived from near-IR data suggests anticyclones to extend vertically from (at least) the water cloud (∼5 bar) up to the tropopause (∼100–200 mbar), and in some cases into the stratosphere.Based upon our observations, we propose that air is rising along the center of a vortex, and descending around the outer periphery, producing the 5-μm bright rings. Observationally, we constrain the maximum radius of these rings to be less than twice the local Rossby deformation radius, L_R. If the radius of the visible oval (i.e., the clouds that make the oval visible) is >3000 km, our observations suggest that the descending part of the secondary circulation must be within these ovals. For the Red Oval BA, we postulate that the return flow is at the location of its red annulus, which has a radius of ∼3000 km.We develop a theory for the secondary circulation, where air is (baroclinically) rising along the center of a vortex in a subadiabatic atmosphere, and descending at a distance not exceeding ∼2× the local Rossby deformation radius. Using this model, we find a timescale for mixing throughout the vortex of order several months, which suggests that the chromophores that are responsible for the red color of Oval BA’s red annulus must be produced locally, at the location of the annulus. This production most likely results from the adiabatic heating in the descending part of the secondary circulation. Such higher-than-ambient temperature causes NH₃–ice to sublime, which will expose the condensation nuclei, such as the red chromophores.     

Differential rotation in a solar-driven quasi-axisymmetric circulation

We consider the concept of a quasi-axisymmetric circulation to explore the global scale dynamics of planetary atmospheres. The momentum and energy transport processes in the smaller scales are formulated in terms of anisotropic eddy diffusion. In the early work of Williams and Robinson (1973) these concepts have been introduced to describe the Jovian circulation. Our study differs in that we adopt a spectral model (with vector spherical harmonics) and consider a linear system; we are also examining a different parameter regime. The troposphere of Jupiter is assumed to be weakly convectively unstable, and the circulation is driven by the fundamental component of solar differential heating with a broad maximum at the equator. Mode coupling arising from the Coriolis action is considered in self consistent form, and momentum and energy are allowed to cascade from lower to higher order modes. With a limited number of spherical harmonics, up to order 40, and with homogeneous boundary conditions, the conservation equations are integrated between the 25 and 10^–5 bar pressure levels. In addition, a simplified single layer model is discussed which, even though heuristic in nature, elucidates and complements the numerical results. Our analysis leads to the following conclusions: (a) For a negative stability, S ₀ = T ₀/r + , the energy transports arising from large scale advection by the meridional circulation can amplify the response to the external heating. This crucially depends on the latitudinal structure of the circulation, so that banded wind fields with equatorial zonal jets are preferentially excited. (b) With a negative stability of order S ₀ ~ – 10^–6 K cm^–1, the computed number of positive (and negative) zonal jets is similar to that observed on Jupiter. (c) The observed magnitudes in the zonal wind velocities require that the vertical eddy diffusion coefficient is of the order K _r ~ 3 × 10⁵ cm² s^–1, which in turn is consistent with the observed outward flux of energy from the planetary interior (F K _r S ₀ ); this diffusion rate is also of the right order of magnitude to obey mixing length theory. (d) The ratio between the horizontal and vertical eddy diffusion coefficients (relative mixing factor) is of critical importance. If it is too large ( 10⁵), differential rotation or alternating zonal jets cannot be maintained; if it is too small ( 10⁴), the equator tends to corotate. The intermediate value of order R ~ 5 × 10⁴ is again consistent with mixing length theory. (e) With the above constraints on the transport coefficients, the flow is quasigeostrophic. (f) The meridional circulation is multicellular and of the Ferrel-Thomson type. It is consistent with the observed cloud striations in the Jovian atmosphere. (g) In the stable stratosphere at higher altitudes the fundamental component, directly driven by the Sun, dominates. The circulation degenerates, and broad, positive zonal jets develop at middle latitudes, resembling the observed wind field in the visible cloud cover of the Venus atmosphere.Applied Research Corporation, Landover, Maryland, U.S.A.     

Deep jets on gas-giant planets

Three-dimensional numerical simulations of the atmospheric flow on giant planets using the primitive equations show that shallow thermal forcing confined to pressures near the cloud tops can produce deep zonal winds from the tropopause all the way down to the bottom of the atmosphere. These deep winds can attain speeds comparable to the zonal jet speeds within the shallow, forced layer; they are pumped by Coriolis acceleration acting on a deep meridional circulation driven by the shallow-layer eddies. In the forced layer, the flow reaches an approximate steady state where east-west eddy accelerations balance Coriolis accelerations acting on the meridional flow. Under Jupiter-like conditions, our simulations produce 25 to 30 zonal jets, similar to the number of jets observed on Jupiter and Saturn. The simulated jet widths correspond to the Rhines scale; this suggests that, despite the three-dimensional nature of the dynamics, the baroclinic eddies energize a quasi-two-dimensional inverse cascade modified by the β effect (where β is the gradient of the Coriolis parameter). In agreement with Jupiter, the jets can violate the barotropic and Charney-Stern stability criteria, achieving curvatures ^∂2u/∂y² of the zonal wind u with northward distance y up to 2β. The simulations exhibit a tendency toward neutral stability with respect to Arnol'd's second stability theorem in the upper troposphere, as has been suggested for Jupiter, although deviations from neutrality exist. When the temperature varies strongly with latitude near the equator, our simulations can also reproduce the stable equatorial superrotation with wind speeds greater than . Diagnostics show that barotropic eddies at low latitudes drive the equatorial superrotation. The simulations also broadly explain the distribution of jet-pumping eddies observed on Jupiter and Saturn. While idealized, these simulations therefore capture many aspects of the cloud-level flows on Jupiter and Saturn.     

Hydrodynamic processes of angular momentum transport in the interior of a rotating massive hydrogen-burning star

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.     

An explanation of the persistence of the Great Red Spot of Jupiter

An argument is given basing the persistence of the Great Red Spot of Jupiter on compensation of the natural decay of vorticity by collision with a portion of the vortices shed by the South boundary of the South Tropical Zone. The latter are deviated northward by Coriolis acceleration. The GRS itself is regarded as a Rankine vortex with a central depression revealing the coloration of a layer below.     

Solar heating and internal heat flow on Jupiter

Models of convection in Jupiter's interior are studied to test the hypothesis that internal heat balances the absorbed sunlight at each latitude. Such a balance requires that the ratio of total emitted heat to absorbed sunlight be above a critical value 4/π ≈ 1.27. The necessary horizontal heat transport then takes place in the interior instead of in the atmosphere. Regions of stable stratification can arise in the interior owing to the effects of solar heating and rotation. In such regions, upward heat transfer takes place on sloping surfaces, as in the Earth's atmosphere, provided there are horizontal temperature gradients. Potential temperature gradients are found to be small, and the time constant for the pattern to reach equilibrium is found to be short compared to the age of the solar system. It is suggested that Jupiter and Saturn owe their axisymmetric appearance to internal heat flow, which eliminates differential heating in the atmosphere that would otherwise drive meridional motions.     

Meridional energy balance of Jupiter

The meridional energy balance of Jupiter is calculated from high spatial resolution observations by the Voyager 1 infrared spectrometer and radiometer. On a hemispheric scale Jupiter radiates thermal energy to space approximately uniform with latitude while solar energy absorption varies approximately as the solar angle. This implies internal adjustment to the solar energy with a larger contribution poleward of ±45° than in the equatorial zone. The internal flux is modulated by the major visible features of the zone and belt system but, unlike the hemispheric scale where increased internal flux is correlated with decreased solar absorption, on smaller scales the inverse occurs. The energy balance is very likely to be controlled by dynamics, but the relative influence of the upper atmosphere and the interior is not yet clear. Models have been proposed that would explain the pole-to-equator variation in the thermal emission and it is suggested that the smaller scale variations may be the result of forced convective circulation.     

Hadley circulations and Kelvin wave-driven equatorial jets in the atmospheres of Jupiter and Saturn

We propose a dynamical mechanism that can plausibly explain the origin of the broad prograde equatorial winds observed on Jupiter and Saturn, and examine the feasibility of this mechanism using two- (2D) and three-dimensional (3D) numerical simulation models. The idea is based on combining a narrow Gaussian jet peaking at the equator, which is induced by the momentum transfer from an upward propagating equatorial Kelvin-wave, and a pair of off-equatorial jets due to a meridional-vertical circulation similar to the tropical Hadley circulation on Earth. We employ for this feasibility study a 2D mechanistic mean-flow model which incorporates the influence of prescribed waves, and a 3D general circulation model, based on the generalised primitive equations of atmospheric motion. We then confirm that the dynamical models of both kinds can successfully reproduce theoretically expected flows of a reasonable magnitude, and that when two mechanisms are combined, a broad super-rotating jet is produced with off-equatorial maxima in zonal velocity for both Jupiter and Saturn, approximately in accordance with observations.     

Large-scale motions in the sun

Large-scale solar motions comprise differential rotation (with latitudinal, and perhaps radial gradients), axially symmetric meridional motions, and possible asymmetric motions (giant convective cells or Rossby-type waves or both). These motions must be basic in any satisfactory theory of the changing pattern of solar magnetic fields and of the 22-yr cycle. In the present paper available data are discussed and, as far as possible, evaluated and explained.Rotational measurements are based on the changing positions of discrete features such as sunspots, on Doppler shifts, on geophysical changes and on statistical evaluation of the motions of diffuse objects. The first mentioned, comprising faculae, sunspots, K-corona (to latitudes 45°) and filaments, show agreement better than 0.7 %. A new formula for surface rotation _s , based on faculae and sunspot data, is _s = 14.52 – 2.48 sin² b – 2.51 sin⁶ b deg day^–1, where b is latitude, and validity may extend to about 70°. Errors in Doppler shift measurements and statistical treatments are discussed. There is evidence of a much slower coronal rate at high latitudes, and of a slower sub-surface rate at lower latitudes.Ordered meridional motions have been revealed by statistical investigations of the positions of spot groups, of spots and of filaments. All these results seem explicable in terms of an oscillating hydro-magnetic circulation in each hemisphere. These have both 11-yr and 22-yr components, and these periods are provided by a general dipole field of about one gauss, together with a pair of toroidal fields centred at latitudes ±16° and of average strength of order 10 G.Evidence of large-scale (perhaps 3 × 10⁵ km), irregular surface motions is provided by the distribution of surface magnetic flux, the motions of sunspots, and Doppler-shift observations; it is supported by Ward's theory of the equatorial acceleration. The possibility is suggested that these asymmetric motions also drive the oscillatory meridional motions.     

UV and IR auroral emission model for the outer planets: Jupiter and Saturn comparison

Planetary aurora display the dynamic behavior of the plasma gas surrounding a planet. The outer planetary aurora are most often observed in the ultraviolet (UV) and the infrared (IR) wavelengths. How the emissions in these different wavelengths are connected with the background physical conditions are not yet well understood. Here we investigate the sensitivity of UV and IR emissions to the incident precipitating auroral electrons and the background atmospheric temperature, and compare the results obtained for Jupiter and Saturn. We develop a model which estimates UV and IR emission rates accounting for UV absorption by hydrocarbons, ion chemistry, and non-LTE effects. Parameterization equations are applied to estimate the ionization and excitation profiles in the H₂ atmosphere caused by auroral electron precipitation. The dependences of UV and IR emissions on electron flux are found to be similar at Jupiter and Saturn. However, the dependences of the emissions on electron energy are different at the two planets, especially for low energy (<10 keV) electrons; the UV and IR emissions both decrease with decreasing electron energy, but this effect in the IR is less at Saturn than at Jupiter. The temperature sensitivity of the IR emission is also greater at Saturn than at Jupiter. These dependences are interpreted as results of non-LTE effects on the atmospheric temperature and density profiles. The different dependences of the UV and IR emissions on temperature and electron energy at Saturn may explain the different appearance of polar emissions observed at UV and IR wavelengths, and the differences from those observed at Jupiter. These results lead to the prediction that the differences between the IR and UV aurora at Saturn may be more significant than those at Jupiter. We consider in particular the occurrence of bright polar infrared emissions at Saturn and quantitatively estimate the conditions for such IR-only emissions to appear.     

Seasonal variation of Titan's atmospheric structure simulated by a general circulation model.

The seasonal variation of Titan's atmospheric structure with emphasis on the stratosphere is simulated by a three-dimensional general circulation model. The model includes the transport of haze particles by the circulation. The likely pattern of meridional circulation is reconstructed by a comparison of simulated and observed haze and temperature distribution. The GCM produces a weak zonal circulation with a small latitudinal temperature gradient, in conflict with observation. The direct reason is found to be the excessive meridional circulation. Under uniformly distributed opacity sources, the model predicts a pair of symmetric Hadley cells near the equinox and a single global cell with the rising branch in the summer hemisphere below about z = 230 km and a thermally indirect cell above the direct cell near the solstice. The interhemispheric circulation transports haze particles from the summer to the winter hemisphere, causing a maximum haze opacity contrast near the solstice and a smaller contrast near the equinox, contrary to observation. On the other, if the GCM is run under modified cooling rate in order to account for the enhancement in nitrites and some hydrocarbons in the northern hemisphere near the vernal equinox, the meridional cell at the equinox becomes a single cell with rising motions in the autumn hemisphere. A more realistic haze opacity distribution can be reproduced at the equinox. However, a pure transport effect (without particle growth by microphysics, etc.) would not be able to cause the observed discontinuity of the global haze opacity distribution at any location. The stratospheric temperature asymmetry can be explained by a combination of asymmetric radiative heating rates and adiabatic heating due to vertical motion within the thermally indirect cell. A seasonal variation of haze particle number density is unlikely to be responsible for this asymmetry. It is likely that a thermally indirect cell covers the upper portion of the main haze layer. An artificial damping of the meridional circulation enables the formation of high-latitude jets in the upper stratosphere and weaker equatorial superrotation. The latitudinal temperature distribution in the stratosphere is better reproduced.     

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.     

Meridional Motions and Reynolds Stress Determined by Using Kanzelhöhe Drawings and White Light Solar Images from 1964 to 2016

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.     

Zonal mean circulation at the cloud level on Venus: Spring and fall 1979 OCPP observations

Cloud motions were obtained from a number of images acquired in reflected solar ultraviolet light during spring and fall of 1979 from the Pioneer Venus Orbiter Cloud Photopolarimeter (OCPP) to determine the zonal mean circulation of the atmosphere of Venus at the cloud top level. The meridional profile of the zonal component of motion is somewhat different from that previously obtained from Mariner 10 and preliminary Pioneer Venus observations, although the equatorial magnitude is about the same (?94 m/sec). The mean meridional motion is toward the south pole south of about 5° south latitude, and toward the north pole north of this latitude, with peak mean magnitudes of about 7 m/sec polewards of 20° north and 40° south latitudes in the respective hemispheres. From the few measurements obtained at higher latitudes the magnitude of the mean meridional component appears to decrease although it is still directed toward the respective poles. Due to the evolution of the cloud patterns over the duration of the images from which the cloud velocities are obtained, the uncertainties in the mean zonal and meridional components may be as large as 5–10 and 2–4 m/sec, respectively. Preliminary estimates of meridional momentum transport show that the mean circulation dominates the eddy circulation transport completely, in agreement with the estimates obtained from Mariner 10 data, although the uncertainties in both the mean and eddy circulation transports are large. The momentum transports are polewards and their peak magnitudes occur at latitudes between 20° and 40° in both the hemispheres.     

Meridional motions of magnetic features in the solar photosphere

We cross-correlate pairs of Mt. Wilson magnetograms spaced at intervals of 24–38 days to investigate the meridional motions of small magnetic features in the photosphere. Our study spans the 26-yr period July 1967–August 1993, and the correlations determine longitude averages of these motions, as functions of latitude and time. The time-average of our results over the entire 26-yr period is, as expected, antisymmetric about the equator. It is poleward between 10° and 60°, with a maximum rate of 13 m s^–1, but for latitudes below ±10° it is markedly equatorward, and it is weakly equatorward for latitudes above 60°. A running 1-yr average shows that this complex latitude dependence of the long-term time average comes from a pattern of motions that changes dramatically during the course of the activity cycle. At low latitudes the motion is equatorward during the active phase of the cycle. It tends to increase as the zones of activity move toward the equator, but it reverses briefly to become poleward at solar minimum. On the poleward sides of the activity zones the motion is most strongly poleward when the activity is greatest. At high latitudes, where the results are more uncertain, the motion seems to be equatorward except around the times of polar field reversal. The difference-from-average meridional motions pattern is remarkably similar to the pattern of the magnetic rotation torsional oscillations. The correspondence is such that the zones in which the difference-from-average motion is poleward are the zones where the magnetic rotation is slower than average, and the zones in which it is equatorward are the zones where the rotation is faster.Our results suggest the following characterization: there is a constant and generally prevailing motion which is perhaps everywhere poleward and varies smoothly with latitude. On this is superimposed a cycle-dependent pattern of similar amplitude in which the meridional motions of the small magnetic features are directed away from regions of magnetic flux concentration. This is suggestive of simple diffusion, and of the models of Leighton (1964) and Sheeley, Nash, and Wang (1987). The correspondence between the meridional motions pattern and the torsional oscillations pattern in the magnetic rotation suggests that the latter may be an artifact of the combination of meridional motion and differential rotation.     

Inhomogeneous convection and the equatorial acceleration of the sun

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.     

On the Sun's differential rotation and pole-equator temperature difference

The Sun's differential rotation can be understood in terms of a preferential stabilization of convection (by rotation) in the polar regions of the lower part of the convection zone (where the Taylor number is large). A significant pole-equator difference in flux () can develop deep inside the convection zone which would be unobservable at the surface, because can be very efficiently reduced by large scale meridional motions rising at the poles and sinking at the equator. This is the sense of circulation needed to produce the observed equatorial acceleration of the Sun. Differential rotation is generated, therefore, in the upper part of the convection zone (where the interaction of rotation with convection is small) and results as the convection zone adjusts to a state of negligible Taylor number.The National Center for Atmospheric Research is sponsored by the National Science Foundation.