Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Geothermal palaeogradients and metamorphic zonation from the conodont colour alteration index (CAI)

The conodont colour alteration index (CAI) is potentially valuable in thermal history investigations, but there are problems in its use. An approach is proposed herein to overcome the problem of establishing reliable geothermal palaeogradients in areas with burial metamorphism, based on knowledge of the stratigraphic succession thickness, the boundaries of chronostratigraphic units, and the age and duration of deformation episodes. Although also problematical that a correlation between CAI and Kübler index (KI) values does not exist, there are areas where CAI and KI values are notably consistent for the anchizone boundaries; however, anomalous correlations between CAI and KI values have also been found in some areas. A CAI anchizone (or ancaizone) is defined in order to enable CAI values to be used independently to establish a metamorphic zonation.     

Lead isotope systematics of Late Cretaceous – Tertiary Andean arc magmas and associated ores between 8°N and 40°S: evidence for latitudinal mantle heterogeneity beneath the Andes

ABSTRACT Lead isotope variability of magmatic arc rocks and associated mineralization of the Central Andes is usually considered to be the result of mixing between a homogeneous mantle and heterogeneous continental crust. About 230 new lead isotope data on the Northern and Central Andes allow us to compare for the first time lead isotope systematics of the Late Cretaceous – Tertiary arc magmatism and associated mineralization along the Andean chain between 8°N and 40°S. Lead isotope compositions indicate mixing between mantle and upper crustal rocks along the whole Andean chain. Additionally, we have found that mantle end-members of the Late Cretaceous – Tertiary magmatism are heterogeneous and systematically shifted towards less radiogenic ²⁰⁶Pb/²⁰⁴Pb compositions from north to south along the Andes. This heterogeneity most likely results from mixing between a low radiogenic mantle, possibly carrying a DMM or EM I component, and a more radiogenic mantle, possibly carrying an HIMU component. Thus, our results imply that lead isotope variability of Andean magmas at the continental scale is caused not only by crustal but also by mantle heterogeneity.     

Late Quaternary vegetation changes around Lake Rutundu,Mount Kenya,East Africa: evidence from grass cuticles,pollen and stable carbon isotopes

Woody, subalpine shrubs and grasses currently surround Lake Rutundu, Mount Kenya. Multiple proxies, including carbon isotopes, pollen and grass cuticles, from a 755‐cm‐long core were used to reconstruct the vegetation over the past 38 300 calendar years. Stable carbon‐isotope ratios of total organic carbon and terrestrial biomarkers from the lake sediments imply that the proportion of terrestrial plants using the C₄ photosynthetic pathway was greater during the Late Pleistocene than in the Holocene. Pollen data show that grasses were a major constituent of the vegetation throughout the Late Pleistocene and Holocene. The proportion of grass pollen relative to the pollen from other plants was greatest at the last glacial maximum (LGM). Grass cuticles confirm evidence that C₄ grass taxa were present at the LGM and that the majority followed the cold‐tolerant NADP‐MEC₄ subpathway. Copyright © 2003 John Wiley & Sons, Ltd.