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.     

Baroclinic instabilities in Jupiter's zonal flow

The baroclinic stability of Jupiter's zonal flow is investigated using a model consisting of two continuously stratified fluid layers. The upper layer, containing a zonal shear flow and representing the Jovian cloudy regions above p ～ 5 bars, is the same as Eady's (1949) model for the Earth. The lower layer has a relatively large but finite depth with a quiescent basic state, representing the deep Jovian fluid bulk below p ～ 5 bars. Due to the presence of the lower layer, the linearized non-dimensional growth rates are drastically reduced from the O(1) growth rates of the original Early model. Only very long wavelengths relative to the upper fluid's radius of deformation L₁ are unstable. Eddy transports of heat are also reduced relative to estimates based on scaling arguments alone. Since the hydrostatic approximation for the lower-layer perturbation breaks down at great depths, a second model is presented in which energy propagates downward in an infinitely deep lower fluid obeying the full linearized fluid equations. In this model, the growth rates are again very small, but now all wavelengths are unstable with maximum growth rates occurring for wavelengths O(1) relative to L₁. These results illustrate the importance for the upper-layer meteorology of the interface boundary condition with the lower fluid, which is radically different from the rigid lower boundary of the Earth's troposphere.     

Photoelectric lightcurves of asteroids 42 Isis, 45 Eugenia, 56 Melete, 103 Hera, 532 Herculina,and 558 Carmen

Photoelectric observations of six asteroids are presented. The following synodic periods of rotation and amplitudes of variation are reported: 42 Isis, P = 13^h.59, Δm = 0.32; 45 Eugenia, P = 5^h.70, Δm = 0.30; 56 Melete, P = 13^h.7 or 19^h.0, Δm = 0.06; 532 Herculina, P = 9^h.408, Δm = 0.15; 558 Carmen, P ≈ 10^h, Δm ≈ 0.25. The asteroid 103 Hera exhibited no periodic variation in excess of about 0.03 magnitude. The period found for 532 Herculina is one half that previously reported by other observers.     

Photoelectric lightcurve and period of rotation of the asteroid 182 Elsa

Photoelectric observations on five consecutive nights yield a period of rotation of 80 ± 2 hr with an amplitude of 0.7 magnitude for 182 Elsa, making it the longest period of rotation known to date. 182 Elsa is classed as an S object with a diameter of 48 km.     

Asteroid rotation: III. 1978 Observations

Photoelectric observations of 32 asteroids observed from Table Mountain Observatory during the second half of 1978 are reported. Rotation periods were obtained for most objects. Absolute magnitudes and phase functions were not determined for any of these asteroids. The geometric mean rotation period of the 32 asteroids observed is 14.2 ± 1.6 hr, as compared to 9.38 ± 0.35 hr for 182 asteroids analyzed in Paper I (A. W. Harris and J. A. Burns, 1979, Icarus 40, 115–144). We attribute this difference to an observational selection effect which favors detection of fast rotation, as discussed in Paper I. If this is true, then the present sample contains the reverse bias, since it is complete in that a period (in some cases very approximate) was obtained for each object observed, but fast rotators are underrepresented due to prior discovery of their rotation properties.     

Vertical extent of zonal winds on Venus

Possible interrelationships of different observations have been studied to clear up some obvious inconsistencies and develop a coherent picture of the kinematics of the Venus atmosphere. There is a wind shear in the vicinity of 60 km with vertical dimensions on the order of a scale height. The kinematical model has negligible surface winds, speeds increasing with altitude to approximately 45 km, a layer of high-speed retrograde zonal winds extending from approximately 45 to 60 km, a wind shear between 60 and 65 km, and slow atmospheric motions above this. Spacecraft data show that the region of high-speed winds is thicker on the day side of the planet than on the night side.     

Interactive effects of the type of milling media and CuSO4 addition on the flotation performance of sulphide minerals from Merensky ore Part II: Froth stability

The limitations of pulp chemistry measurements in the flotation of a platinum group mineral (PGM) bearing Merensky ore were demonstrated in Part 1 of this article. In this paper the importance of the contribution of the froth structure due to changing froth stability is analysed using the batch flotation data. The effects of mild steel (MS) and stainless steel (SS) milling media and the addition of copper sulphate on the flotation performance of the sulphide minerals in Merensky ore have been evaluated in relation to the changes in stability of the froth phase. The effects of pulp chemistry and froth stability on the flotation of sulphide minerals were distinguished by using two different rate constants (k_t and k_w). The rate constant (k_w) calculated as a function of cumulative water recovery was used to describe characteristics of froth phase and k_t was calculated as a function of flotation time. The results revealed that the type of grinding media and copper sulphate addition had an interactive effect on the froth stability. While mild steel (MS) milling increased the froth stability due to the presence of hydrophilic iron hydroxides and colloidal metallic iron, the addition of copper sulphate reduced the stability, especially with stainless steel (SS) milling. Copper sulphate addition had a dual role in the flotation of Merensky ore in that it caused destabilisation of the froth zone as well as activation of selected sulphide minerals. The dominant effect was found to depend on the type of milling media and floatability of the mineral in question and this work has demonstrated the importance of using a combination of measurements to evaluate flotation performance holistically.     

First record of a Cretaceous cheilostome bryozoan from Hokkaido, Japan

A small collection of recrystallised, encrusting colonies of a single species from the Mikasa Formation (lower Middle Cenomanian), represents the first record of cheilostome (malacostegan or anascan) bryozoans from Hokkaido, Japan.     

An investigation of upper mantle heterogeneity beneath the Archaean and Proterozoic crust of western Canada from Lithoprobe controlled-source seismic experiments

Observations of upper mantle reflectivity at numerous locations around the world have been linked to the presence of a heterogeneous distribution of rock types within a broad layer of the upper mantle. This phenomenon is observed in wide-angle reflection data from Lithoprobe's Alberta Basement Transect [the SAREX and Deep Probe experiments of 1995] and Trans-Hudson Orogen Transect [the THoRE experiment of 1993]. SAREX and Deep Probe image the Archaean lithosphere of the Hearne and Wyoming Provinces, whereas THoRE images the Archaean and Proterozoic lithosphere of the Trans-Hudson Orogen and neighbouring areas.Finite-difference synthetic seismograms are used to constrain the position and physical properties of the reflective layer. SAREX/Deep Probe modelling uses a 2-D visco-elastic finite-difference routine; THoRE modelling uses a pseudospectral algorithm. In both cases, the upper mantle is parameterized in terms of two media. One medium is the background matrix; the other is statistically distributed within the first as a series of elliptical bodies. Such a scheme is suitable for modelling: (1) variations in lithology (e.g., a peridotite matrix with eclogite lenses) or (2) variations in rheology (e.g., lenses of increased strain within a less strained background).The synthetic seismograms show that the properties of heterogeneities in the upper mantle do not change significantly between the two Lithoprobe transects. Beneath the Trans-Hudson Orogen in Saskatchewan, the layer is best modelled to lie at depths between 80 and 150 km. Based on observations from perpendicular profiles, anisotropy of the heterogeneities is inferred. Beneath the Precambrian domains of Alberta, 400 km to the west, upper mantle heterogeneities are modelled to occur between depths of 90 and 140 km. In both cases the heterogeneous bodies within the model have cross-sectional lengths of tens of kilometers, vertical thicknesses less than 1 km, and velocity contrasts from the background of − 0.3 to − 0.4 km/s. Based on consistency with complementary data and other results, the heterogeneous layer is inferred to be part of the continental lithosphere and may have formed through lateral flow or deformation within the upper mantle.     

Monte Carlo simulation of mixing in Ca3Fe2Ge3O12–Ca4Ge4O12 garnets and implications for the thermodynamic stability of pyrope–majorite solid solution

Static lattice energy calculations, based on empirical pair potentials, were performed for a large set of structures differing in the arrangement of octahedral cations within the garnet 2 × 2 × 2 supercell. The compositions of these structures varied between Ca₃Fe₂Ge₃O₁₂ and Ca₄Ge₄O₁₂. The energies were cluster expanded using pair and quaternary terms. The derived ordering constants were used to constrain Monte Carlo simulations of temperature-dependent mixing properties in the ranges of 1,073–3,673 K and 0–10 GPa. The free energies of mixing were calculated using the method of thermodynamic integration. The calculations predict a wide miscibility gap between Fe-rich (cubic) and Fe-pure (tetragonal) garnets consistent with recent experimental observations of Iezzi et al. (Phys Chem Miner 32:197–207, 2005). It is shown that the miscibility gap arises due to a very strong cation ordering at the Fe-pure composition, driven by the charge difference between Ca²⁺ and Ge⁴⁺ cations. The structural and thermodynamic analogies between Ca–Ge and Mg–Si systems suggest that a similar miscibility gap should exist between pyrope and Mg–Si-majorite.