Numerical simulation of the final stages of terrestrial planet formation

Three representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are presented. The mass and relative-velocity distributions of the bodies in these simulations are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies, therefore, arise in a natural way and the assumption of expressions for the relative velocity distribution and the gravitational collision cross section is unnecessary. These simulations indicate that the growth of bodies with final masses approaching those of Venus and the Earth is possible, at least for the case of a two-dimensional system. Simulations assuming an initial uniform distribution of orbital eccentricities on the interval from 0 to e_max are found to produce final states containing too many bodies with masses which are too small when e_max < 0.10, while simulations with e_max > 0.20 result in too many catastrophic collisions between bodies thus preventing rapid accretion of planetary-size bodies. The e_max = 0.15 simulation ends with a state surprisingly similar to that of the present terrestrial planets and, therefore, provides a rough estimate of the range of radial sampling to be expected for the terrestrial planets.     

Stable isotope (O and C) and pollen trends in eastern Lake Erie,evidence for a locally-induced climatic reversal of Younger Dryas age in the Great Lakes basin

A cool period from about 11000 to 10 500 BP (11 to 10.5 ka) is recognized in pollen records from the southern Great Lakes area by the return of Picea and Abies dominance and by the persistence of herbs. The area of cooling appears centred on the Upper Great Lakes. A high-resolution record (ca. 9 mm/y) from a borehole in eastern Lake Erie reveals, in the same time interval, this pollen anomaly, isotope evidence of meltwater presence (a — 3 per mil shift in ¹⁸O and a +1.1 per mil shift in ¹³C), increased sand, and reduced detrital calcite content, all suggesting concurrent cooling of Lake Erie. The onset of cooling is mainly attributed to the effect of enhanced meltwater inflow on the relatively large upstream Main Lake Algonquin during the first eastward discharge of glacial Lake Agassiz. Termination of the cooling coincides with drainage of Lake Algonquin, and is attributed to loss of its cooling effectiveness associated with a substantial reduction in its surface area. It is hypothesized that the cold extra inflow effectively prolonged the seasonal presence of lake ice and the period of spring overturn in Lake Algonquin. The deep mixing would have greatly increased the thermal conductive capacity of this extensive lake, causing suppression of summer surface lakewater temperatures and reduction of onshore growing-degree days. Alternatively, a rapid flow of meltwater, buoyed on sediment-charged (denser) lakewater, may have kept the lake surface cold in summer. Other factors such as wind-shifted pollen deposition and possible effects from the Younger Dryas North Atlantic cooling could have contributed to the Great Lakes climatic reversal, but further studies are needed to resolve their relative significance.Contribution to Climo Locarno — Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate ProgramGeological Survey of Canada Contribution 58 890     

Noble gases in the Allende and Abee meteorites and a gas-rich mineral fraction: investigation by stepwise heating

Noble gases in three meteoritic samples were examined by stepwise heating, in an attempt to relate peaks in the outgassing curves to specific minerals: NeKrXe in Allende (C3V) and an Allende residue insoluble in HF-HCl, and Xe in Abee (E4). In Allende, chromite and carbon contain most of the trapped Ne (²⁰Ne/²²Ne ≈ 8.7) and anomalous Xe enriched in light and heavy isotopes, and release it at ~850°C (bulk meteorite) or 1000°C (residue). Mineral Q, containing most of the trapped Ar, Kr, Xe as well as some Ne (²⁰Ne/²²Ne ≈ 10.4), releases its gases mainly between 1200 and 1600°C, well above the release temperatures of organic polymers (300–500°) or amorphous carbon (800–1000°). The high noble-gas release temperature, ready solubility in oxidizing acids, and correlation with acid-soluble Fe and Cr all point to an inorganic rather than carbonaceous nature of Q.All the radiogenic ¹²⁹Xe is contained in HCl, HF-soluble minerals, and is distributed as follows over the peaks in the release curve: Attend 1000° (75%), 1300° (25%); Abee (data of Hohenberg and Reynolds, 1969) ~850° (15%), 1100° (60%), 1300° (25%). No conclusive identifications of host phases can yet be given; possible candidates are troilite and silicates for Allende, and djerfisherite, troilite and silicates for Abee.Mineral Q strongly absorbs air xenon, and releases some of it only at 800–1000°C. Dilution by air Xe from Q and other minerals may explain why temperature fractions from bulk meteorites often contain less ^124–130Xe for a given enrichment in heavy isotopes than does xenon from etched chromitecarbon samples, although chromite-carbon is the source of the anomalous xenon in either case. Air xenon contamination thus is an important source of error in the derivation of fission xenon spectra.     

Observations of cosmic gamma-ray bursts

The occasional occurrence of brief but intense bursts of cosmic gamma-rays was disclosed through a systematic search of data acquired from the Vela satellites. Confirmation of the nature of the events and additional detail of their characteristics has subsequently been provided by 15 other groups of experimenters with instruments on 13 spacecraft. Thirty-nine such events have been identified from data spanning a period of four and a half years. The record of intensity as a function of time varies considerably for different events, with total durations ranging from 0.1 to 60s. Time-integrated flux density ranges from 10^–6 to 10^–3 erg cm^–2. Spectral measurements have been accomplished by several groups of experimenters, showing a broad maximum in the energy distribution at about 150 keV. The distribution of source directions implies either near galactic or extragalactic locations. The existing data are not sufficient to distinguish between the various models proposed to explain the phenomenon; no model is completely consistent with all observed characteristics.Work performed under the auspices of the United States Energy Research and Development Administration.Paper presented at the COSPAR Symposium on Fast Transients in X-and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Shape and distribution analysis of Merensky Reef potholing, Northam Platinum Mine, western Bushveld Complex: implications for pothole formation and growth

Syn-magmatic removal of the cumulate pile during the formation of the Bushveld Complex resulted in “potholes”. Erosion progressed downward in the cumulate pile, resulting in a series of steep, transgressive contacts between locally conformable potholed reefs in the regional pothole sub-facies of the Swartklip Facies in the western limb of the Bushveld Complex. The deepest of these potholes, “third-order” or “FWP2” potholing, occurs where the base of the Merensky Cyclic Unit transgresses the Upper Pseudo-Reef Chromitite marker horizon. The base of a FWP2 pothole on Northam Platinum Mine consists of an unconformable stringer Merensky Chromitite overlain by a medium-grained, poikilitic orthopyroxenite and underlain by either a pegmatitic harzburgite or the medium-grained Lower Pseudo-Reef Anorthosite. Detailed shape and distribution analysis of FWP2 potholes reveals underlying patterns in their shape and distribution which, in turn, suggest a structural control. The ratio between pothole short vs long axes is 0.624 (N=1,385), although the ratio increases from 0.48 to 0.61 in the long axis range 10 to 60 m, then decreases from 0.61 to 0.57 from 61 to 100 m, increasing again from 0.57 to 0.61 from 101 to 400 m, suggesting that there is not a simple relationship between pothole shape and size. Shape (circularity, eccentricity, and dendricity) analysis of a subset of 638 potholes indicates that potholes with long axes <100 m have an elliptical, average normalized shape, elongate on a 120–150° orientation. Potholes with long axis lengths >100 m have an average normalized shape that is bilobate and elongate on a 120° orientation. The average aspect ratio (short axis length divided by long axis length) of potholes is highest for potholes with long axis lengths >100 m and lowest for potholes with long axis lengths between 35 and 60 m. The most common long axis orientation for potholes with long axis lengths <100 m is 150° but 120° for long axis lengths >100 m. Fractal analysis indicates that the distribution of pothole centers is controlled neither by a single nor several interacting fractal dimensions. Autocorrelation (Fry) analysis of the distribution of pothole centers shows recurring pothole distribution trends at 038, 070, and 110° for potholes over the full range of long axis lengths, while the trends of 008 and 152° occur in potholes with long axes lengths between 60 and 100 m. Chi-squared (X ²) analysis of the locations of pothole centers suggests that the distribution of small potholes is highly non-uniform but becomes exponentially more uniform with increasing pothole size. The model which best fits the observed shape and distribution analysis is a combination of protracted independent growth and “nearest neighbor” merging along specific orientations. For instance, the clustered distribution of original pothole centers resulted in merged potholes with long axes lengths of up to 60 m, exhibiting short vs long axes ratios of 0.61, preferred orientations of 150°, and alignment along 010 and 150° trends. Further independent growth allowed for merging of similar-sized (and smaller) neighboring potholes, generating potholes with long axes of up to 100 m in length, a preferred long axis orientation of 150°, and alignment along 010, 040, 075, and 150°. Subsequent preferential merging occurred along a 120° trend, thereby preserving a bilobate form. This implies that while pothole initiation and enlargement may be driven by a “top-down” (i.e., possibly thermomechanical) process, an underlying linear or structural catalyst/control is revealed in changes in pothole shape during enlargement and, furthermore, in the preferred trends along which potholes merged over a considerable period, possibly concomitant with adjustment of major structures in the footwall to the Bushveld Complex and pulses into the magma chamber.     

Evolution of the Bonneville shoreline scarp in west-central Utah: Comparison of scarp-analysis methods and implications for the diffusion model of hillslope evolution

Wave-cut pluvial shoreline scarps are ideal natural experiments in hillslope evolution because the ages of these scarps are often precisely known and because they form with a range of heights, alluvial textures, and microclimates (i.e., orientation). Previous work using midpoint-slope methods on pluvial scarps in the Basin and Range concluded that scarp evolution is nonlinear and microclimatically controlled. The purpose of this study was to further examine the influence of scarp height, texture and microclimate in an attempt to calibrate a nonlinear model of scarp evolution. To do this, over 150 profiles of the Bonneville shoreline in the adjacent Snake and Tule Valleys, west-central Utah were collected and analyzed by fitting the entire scarp profile to diffusion-equation solutions, taking into account uncertainty in the initial scarp angle. In contrast to previous studies, this analysis revealed no evidence for nonlinearity or microclimatic control. To understand the reason for this discrepancy, we undertook a systematic study of the accuracy of each scarp-analysis method. The midpoint-slope-inverse method was found to yield biased results, with systematically higher diffusion ages for young, tall scarps. The slope-offset method is unbiased but has limited resolution because it requires many scarp profiles to yield a single diffusion age. A method that incorporates the full scarp profile and uncertainty in the initial scarp angle was found to be the most accurate technique. The application of the full-scarp method to the Bonneville shoreline supports the use of a linear diffusion model for scarps up to 20 m in height. Scarp orientation had no discernable effect on diffusivity values. Soil texture was found to have a weak but significant inverse relationship with diffusivity values.     

Mixing and differentiation in the Oruanui rhyolitic magma, Taupo, New Zealand: evidence from volatiles and trace elements in melt inclusions

Large pyroclastic rhyolites are snapshots of evolving magma bodies, and preserved in their eruptive pyroclasts is a record of evolution up to the time of eruption. Here we focus on the conditions and processes in the Oruanui magma that erupted at 26.5 ka from Taupo Volcano, New Zealand. The 530 km³ (void-free) of material erupted in the Oruanui event is comparable in size to the Bishop Tuff in California, but differs in that rhyolitic pumice and glass compositions, although variable, did not change systematically with eruption order. We measured the concentrations of H₂O, CO₂ and major and trace elements in zoned phenocrysts and melt inclusions from individual pumice clasts covering the range from early to late erupted units. We also used cathodoluminescence imaging to infer growth histories of quartz phenocrysts. For quartz-hosted inclusions, we studied both fully enclosed melt inclusions and reentrants (connecting to host melt through a small opening). The textures and compositions of inclusions and phenocrysts reflect complex pre-eruptive processes of incomplete assimilation/partial melting, crystallization differentiation, magma mixing and gas saturation. ‘Restitic’ quartz occurs in seven of eight pumice clasts studied. Variations in dissolved H₂O and CO₂ in quartz-hosted melt inclusions reflect gas saturation in the Oruanui magma and crystallization depths of ∼3.5–7 km. Based on variations of dissolved H₂O and CO₂ in reentrants, the amount of exsolved gas at the beginning of eruption increased with depth, corresponding to decreasing density with depth. Pre-eruptive mixing of magma with varying gas content implies variations in magma bulk density that would have driven convective mixing. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Near Wall Flow over Urban-like Roughness

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s^-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves.The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.     

Near-Wall Flow Development After A Step Change In Surface Roughness

An experimental study of the initial flow field downstream of a step change in surface roughness is presented. The roughness length of the downstream surface was approximately tenfold that of the upstream roughness and, unlike all previous studies, attention was concentrated on the roughness sublayer region beneath the inertial (log-law) region. The experiments were conducted at a boundary layer Reynolds number of about 6 × 10⁴ (based on layer thickness andfree-stream velocity) and around a longitudinal location where the (downstream) roughness length, z_o2, was about 1% of the boundary-layer thickness atthe roughness change point.The thickness of the roughness sublayer was found for the two roughness. It was observed that the vertical profiles of mean velocity and turbulence characteristics started to show similarity after about 160z₀₂ downstream of the roughness change. The presence of a shear stress overshoot is shown to depend strongly on the precise location (with respect to the roughness elements) at which the measurements are made and the thickness of the equilibrium layer is shown to be very sensitive to the way it is defined. It is demonstrated that the growing equilibrium layer has first to encompass the roughness sublayer before any thickness of inertial sublayer can be developed. It follows that, in somepractical cases, like flows across some urban environments, the latter(log-law) region may never exist at all.