Convection in a rotating deep compressible spherical shell: Application to the Sun

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.     

Evaluation of pseudostatic active earth pressure coefficient of cantilever retaining walls

A stress plasticity solution is proposed for evaluating the gravitational and dynamic active earth pressures on cantilever retaining walls with long heel. The solution takes into account the friction angle of the soil, wall roughness, backfill inclination and horizontal and vertical seismic accelerations. It is validated by means of the comparison with both traditional limit equilibrium methods (e.g. Mononobe–Okabe equations) and static and pseudostatic numerical FLAC analyses. For numerical analyses the soil is modelled as an elasto-plastic non-dilatant medium obeying the Mohr–Coulomb yield criterion, while the wall is elastic. The solutions for the horizontal and vertical seismic coefficients are proposed, which allow one to determine the intensity of the active thrust and its inclination δ with respect to the horizontal. It is demonstrated that the latter also depends on the soil friction angle φ. The inclination in seismic conditions δ_E is greater than the one in static conditions, δ_S, usually adopted in both cases. As a matter of fact, since wall stability conditions improve with the increase of inclination δ, the present method gives solutions that are less onerous than traditional ones, producing less conservative wall designs. Finally pseudostatic results are compared with proper dynamic analyses (by FLAC code) performed utilising four Italian accelerometric time-histories as input ground motion.     

Differential rotation set up by latitude-dependent heat transport

Abstract

Models of differentially rotating compressible deep spherical shells are computed according to the method of Belvedere and Paternò (1977): the heat transport is entirely convective, small-scale motions are parametrized by a thermal diffusivity and a kinematic viscosity, and the limit of slow rotation and large viscosity is considered.

In order to adapt the resulting differential rotation to the observed equatorial acceleration of the Sun, the heat transport must be more effective in the vicinity of the equator. In all models the latitude dependence of the transport coefficient induces meridional circulation in the form of a large cell, with rising material at high latitudes and sinking material near the equator. On top of this cell, one or two thin countercells develop in a minority of cases. Large pole-equator temperature differences and meridonal velocities at the surface are obtained when the Prandtl number is 1. But values of, say, 1/10 are sufficiently small to allow the models to be applied to the Sun. In general an angular velocity increasing with depth is found, and the surfaces of constant angular velocity are inclined towards greater depth and higher latitude.     

Petrogenesis of the early Cretaceous Valle Chico igneous complex (SE Uruguay): Relationships with Paraná–Etendeka magmatism

The early Cretaceous (130 Ma) igneous complex of Valle Chico (SE Uruguay) is made up of felsic plutonic and subordinate volcanic rocks and dykes cropping out over an area of about 250 km². This complex is strictly linked with the formation of the Paraná–Etendeka Igneous Province and the first stages of the South Atlantic Ocean rifting. The plutonic rocks range from quartz-monzonite to syenite, quartz-syenite and granite. The volcanic rocks and the dykes range from quartz-latite to trachyte and rhyolite; no substantial differences in term of chemical composition have been found between plutonic and volcanic rocks. Only a sample of basaltic composition (with tholeiitic affinity) has been sampled associated with the felsic rocks. The Agpaitic Index of the Valle Chico felsic rocks range from 0.72 to 1.34, with the peralkaline terms confined in the most evolved samples (SiO₂>65 wt.%). Initial ⁸⁷Sr/⁸⁶Sr₍₁₃₀₎ of the felsic rocks range from 0.7046 to 0.7201, but the range of ⁸⁷Sr/⁸⁶Sr of low-Rb/Sr samples cluster at 0.7083; ¹⁴³Nd/¹⁴⁴Nd₍₁₃₀₎ ratios range from 0.5121 (syenite) to 0.5117 (granite). The tholeiitic basalt show more depleted isotopic compositions (⁸⁷Sr/⁸⁶Sr₍₁₃₀₎=0.7061; ¹⁴³Nd/¹⁴⁴Nd₍₁₃₀₎=0.5122), and plots in the field of other early Cretaceous low-Ti basaltic rocks of SE Uruguay. The radiogenic Sr and unradiogenic Nd of the Valle Chico felsic rocks require involvement of lower crustal material in their genesis either as melt contaminant or as protolith (crustal anatexis). In particular, most of the Valle Chico (VC) felsic rocks define a near-vertical array in Sr–Nd isotopic spaces, pointing toward classical EMI-type composition; this feature is considered to reflect a lower crust involvement as observed for other mafic and felsic rocks of the Paraná–Etendeka Igneous Province. Decompression melting of the lower crust related to Gondwana continental rifting before the opening of the South Atlantic Ocean or the presence of thermal anomalies related to the Tristan plume may have induced the lower crust to partially melt. Alternative hypothesis considers contamination of upper mantle by a mafic/ultramafic keel composed of lower crust and uppermost mantle after delamination and detachment processes. This interaction may have occurred after the continent–continent collision during the last stages of the Panafrican Orogeny. This “lower crust” model does not exclude active involvement of upper crust as contaminant, necessary to explain the strongly radiogenic ⁸⁷Sr/⁸⁶Sr₍₁₃₀₎ isotopic composition of some VC SiO₂-rich rocks. Mineralogical (sporadic presence of pigeonite, Ca–Na and Na clinopyroxene, calcic- and calco-sodic amphibole) and geochemical evidences (major and trace element as well as Sr–Nd isotopic similarities with the felsic early Cretaceous volcanic rocks of the Arequita Formation in SE Uruguay) allow us to propose for the VC rocks a transitional rock series (the most abundant rock types are of syenitic/trachytic composition) preferentially evolving towards SiO₂-oversaturated compositions (granite/rhyolite) also with a strong upper crustal contribution as melt contaminant. This conclusion is in contrast with previous studies according which the VC complex had clear alkaline affinity. Many similarities between VC and the coeval Paresis granitoids (Etendeka, Namibia) are evidenced in this paper. The genetic similarities between VC and the rhyolites (s.l.) of SE Uruguay may find counterparts with the genetic link existing between the early Cretaceous tholeiitic-alkaline Messum complex and the quartz latites (s.l.) of the Awahab Formation (Etendeka region, Namibia).