Adjoint analysis of Buckley-Leverett and two-phase flow equations

This paper analyzes the adjoint equations and boundary conditions for porous media flow models, specifically the Buckley-Leverett equation, and the compressible two-phase flow equations in mass conservation form. An adjoint analysis of a general scalar hyperbolic conservation law whose primal solutions include a shock jump is initially presented, and the results are later specialized to the Buckley-Leverett equation. The non-convexity of the Buckley-Leverett flux function results in adjoint characteristics that are parallel to the shock front upstream of the shock and emerge from the shock front downstream of the shock. Thus, in contrast to the behavior of Burgers’ equation where the adjoint is continuous at a shock, the Buckley-Leverett adjoint, in general, contains a discontinuous jump across the shock. Discrete adjoint solutions from space-time discontinuous Galerkin finite element approximations of the Buckley-Leverett equation are shown to be consistent with the derived closed-form analytical solutions. Furthermore, a general result relating the adjoint equations for different (though equivalent) primal equations is used to relate the two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solutions from space-time discontinuous Galerkin finite element approximations of the two-phase flow equations are observed to obey this relationship.     

Defining the Potential of Nanoscale Re‐Os Isotope Systematics Using Atom Probe Microscopy

Atom probe microscopy (APM) is a relatively new in situ tool for measuring isotope fractions from nanoscale volumes (< 0.01 μm³). We calculate the theoretical detectable difference of an isotope ratio measurement result from APM using counting statistics of a hypothetical data set to be ± 4δ or 0.4% (2s). However, challenges associated with APM measurements (e.g., peak ranging, hydride formation and isobaric interferences), result in larger uncertainties if not properly accounted for. We evaluate these factors for Re‐Os isotope ratio measurements by comparing APM and negative thermal ionisation mass spectrometry (N‐TIMS) measurement results of pure Os, pure Re, and two synthetic Re‐Os‐bearing alloys from Schwander et al. (2015, Meteoritics and Planetary Science, 50, 893) [the original metal alloy (HSE) and alloys produced by heating HSE within silicate liquid (SYN)]. From this, we propose a current best practice for APM Re‐Os isotope ratio measurements. Using this refined approach, mean APM and N‐TIMS ¹⁸⁷Os/¹⁸⁹Os measurement results agree within 0.05% and 2s (pure Os), 0.6–2% and 2s (SYN) and 5–10% (HSE). The good agreement of N‐TIMS and APM ¹⁸⁷Os/¹⁸⁹Os measurements confirms that APM can extract robust isotope ratios. Therefore, this approach permits nanoscale isotope measurements of Os‐bearing alloys using the Re‐Os geochronometer that could not be measured by conventional measurement principles.     

Origin of glacial ridges (OIS 6) in the Kaskaskia Sublobe,southwestern Illinois,USA

The origin of Illinois Episode (OIS 6) glacial ridges (formerly: ‘Ridged Drift’) in the Kaskaskia Basin of southwestern Illinois is controversial despite a century of research. Two studied ridges, containing mostly fluvial sand (OSL ages: ~ 150 ± 19 ka), with associated debris flows and high-angle reverse faults, are interpreted as ice-walled channels. A third studied ridge, containing mostly fine-grained till, is arcuate and morainal. The spatial arrangement of various ridge types can be explained by a glacial sublobe in the Kaskaskia Basin, with mainly fine-grained ridges along the sublobe margins and coarse-grained glaciofluvial ridges in a paleodrainage network within the sublobe interior. Illinois Episode till fabric and striation data demonstrate southwesterly ice flow that may diverge near the sublobe terminus. The sublobe likely formed as glacial ice thinned and receded from its maximum extent. The Kaskaskia Basin contains some of the best-preserved Illinois Episode constructional glacial landforms in the North American midcontinent. Such distinctive features probably result from ice flow and sedimentation into this former lowland, in addition to minimal postglacial erosion. Other similar OIS 6 glacial landforms may exist in association with previously unrecognized sublobes in the midcontinent, where paleo-lowlands might also have focused glacial sedimentation.     

The sources and budget for dissolved sulfate in a fractured carbonate aquifer,southern Sacramento Mountains,New Mexico,USA

Climate change in the SW USA is likely to involve drier conditions and higher surface temperatures. In order to better understand the evolution of water chemistry and the sources of aqueous SO₄ in these semi-arid settings, chemical and S isotope compositions were determined of springs, groundwater, and bedrock associated with a Permian fractured carbonate aquifer located in the southern Sacramento Mountains, New Mexico, USA. The results suggest that the evolution of water chemistry in the semi-arid carbonate aquifer is mainly controlled by dedolomitization of bedrock, which was magnified by increasing temperature and increasing dissolution of gypsum/anhydrite along the groundwater flow path. The δ³⁴S of dissolved SO₄ in spring and groundwater samples varied from +9.0‰ to +12.8‰, reflecting the mixing of SO₄ from the dissolution of Permian gypsum/anhydrite (+12.3‰ to +13.4‰) and oxidation of sulfide minerals (−24.5‰ to −4.2‰). According to S isotope mass balance constraints, the contribution of sulfide-derived SO₄ was considerable in the High Mountain recharge areas, accounting for up to ∼10% of the total SO₄ load. However, sulfide weathering decreased in importance in the lower reaches of the watershed. A smaller SO₄ input of ∼2–4% was contributed by atmospheric wet deposition. This study implies that the δ³⁴S variation of SO₄ in semi-arid environments can be complex, but that S isotopes can be used to distinguish among the different sources of weathering. Here it was found that H₂SO₄ dissolution due to sulfide oxidation contributes up to 5% of the total carbonate weathering budget, while most of the SO₄ is released from bedrock sources during dedolomitization.     

Extreme events as drivers of early human behaviour in Africa? The case for variability,not catastrophic drought

Extreme Late Quaternary climatic events, sometimes of considerable continental extent, are being proposed as major contributors to ancestral human behaviour, particularly migration, in Africa. Most recently, a catastrophic drought in the Afro‐Asian monsoon region has been proposed for 16 000–17 000 years ago, driven by global impacts of the Heinrich event 1 (H1), with potentially significant consequences for Palaeolithic cultures. We provide a new analysis of the assertion and find, on examination of a wide set of palaeoenvironmental records, that the scale and extent of the proposed drought is not supported. While some parts of the African tropics, close to the equator, do appear dry at this time, data for the tropics as a whole suggest markedly variable terrestrial conditions, with some environmental systems experiencing very positive hydrological excursions during H1. We contend that in the quest for evidence of climate drivers of ancestral human behaviour, the variability associated with spatially and temporally complex climatic conditions is a significant factor in itself. Copyright © 2011 John Wiley & Sons, Ltd.     

A thermo‐mechanical model for variably saturated soils based on hypoplasticity

The paper presents a mechanical model for non‐isothermal behaviour of unsaturated soils. The model is based on an incrementally non‐linear hypoplastic model for saturated clays and can therefore tackle the non‐linear behaviour of overconsolidated soils. A hypoplastic model for non‐isothermal behaviour of saturated soils was developed and combined with the existing hypoplastic model for unsaturated soils based on the effective stress principle. Features of the soil behaviour that are included into the model, and those that are not, are clearly distinguished. The number of model parameters is kept to a minimum, and they all have a clear physical interpretation, to facilitate the model usefulness for practical applications. The step‐by‐step procedure used for the parameter calibration is described. The model is finally evaluated using a comprehensive set of experimental data for the thermo‐mechanical behaviour of an unsaturated compacted silt. Copyright © 2011 John Wiley & Sons, Ltd.     

Greatlakean Substage: A replacement for Valderan Substage in the Lake Michigan basin

New evidence from recent field and seismic investigations in the Lake Michigan basin and in the type areas of the Valders, Two Creeks and Two Rivers deposits necessitates revision of late-glacial ice-front positions, rock- and time-stratigraphic nomenclature and climatic interpretations and deglaciation patterns for the period ca. 14,000–7,000 radiocarbon years B.P. The previously reported and long accepted pattern of deglaciation for the Lake Michigan basin started with a regular retreat from the Lake Border Morainic System, with a minor oscillation marked by the Port Huron moraine(s) and then an extensive Twocreekan deglaciation followed by a major (320 km) post-Twocreekan advance (Valders). However, we now record a major retreat between the times of the Lake Border and Port Huron moraines, followed by a gradual retreat from the Port Huron limit and interrupted by a minor standstill (deposition of Manitowoc Till), a retreat (Twocreekan) and a readvance (Two Rivers Till). No Woodfordian or younger readvance was as extensive as had been the preceding one. This sequence argues for a normal, climatically controlled, progressive deglaciation rather than one interrupted by a major post-Twocreekan (formerly Valderan) surge. This revision appears finally to harmonize the geologic evidence and the palynological record for the Great Lakes region. Our investigations show that Valders Till from which the Valderan Substage was named is late-Woodfordian in age. We propose the term “Greatlakean” as a replacement for the now misleading time-stratigraphic term “Valderan”. The type section and the definition of the upper and lower boundaries of the Greatlakean Substage remain the same as those originally proposed for the Valderan Substage but the name is changed.     

On the inter-relationship between grain size sensitive creep and dynamic recrystallization of olivine

The recent theoretical results of Twiss (1976) and Goetze (1978) suggest that at high temperatures and sufficiently high stresses the creep behavior of dry olivine should be dominated by either nonlinear diffusion accommodated grain-boundary sliding or nonlinear Coble creep mechanisms. This would result following the production of a fine grain-size by dynamic recrystallization. For the high-temperature experimental work performed by Karato et al. (1982) dry single crystals of olivine were almost totally recrystallized during creep, and temperature changing experiments were performed on the resulting dynamically recrystallizing polycrystalline aggregates. However, the activation energy for creep determined by Karato et al. (1982) was far higher than that predicted by the models of Twiss (1976) or Goetze (1978), although the conditions required for operation of at least the model of Twiss (1976) apparently were satisfied. The data for the highly recrystallized specimens from the higher stress, lower temperature experiments of Zeuch and Green (1979) and Zeuch (1980) are in good agreement with the results of Karato et al. (1982). These latter experiments were conducted under conditions where either the model of Twiss (1976) or Goetze (1978) should have been applicable. I tentatively conclude that although fine grain sizes were produced in the experiments of Karato et al. (1982), Zeuch and Green (1979) and Zeuch (1980) by dynamic recrystallization, there is no evidence for a transition to grain-boundary diffusional creep mechanisms at high or low stresses despite the predictions of Twiss (1976) or Goetze (1978). Instead, deformation is dominated by dislocation movement with recovery by dynamic recrystallization.