Boussinesq-type modelling using an unstructured finite element technique

A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model.     

Assessing scleractinian corals as recorders for paleo-pH: Empirical calibration and vital effects

Laboratory experiments on the branching, symbiont-bearing coral genus Porites and Acropora have been carried out to determine the dependence of the skeletal boron isotopic composition (δ¹¹B) on the pH of seawater. The results show a clear relationship similar to previously established empirical calibrations for planktonic foraminifera and inorganic calcite. A −0.6‰ offset exists between P. cylindrica and A. nobilis which is systematic over the pH range of 7.7-8.2. To test whether the δ¹¹B of coral skeletons changes with physiological processes such as photosynthesis and respiration, corals were grown along a depth transect in their natural environment and under controlled conditions in the laboratory at varying light intensities and food supply. Although we also observe an isotopic offset between P. compressa and Montipora verrucosa, neither experimental treatment systematically changed the δ¹¹B of the two species. These findings are encouraging for using the boron isotope paleo-pH proxy in corals, because it appears that seawater pH is the dominant control on the boron isotopic composition in corals.     

Wintertime rates of net primary production and nitrate and ammonium uptake in the southern Benguela upwelling system

The elevated levels of primary productivity associated with eastern boundary currents are driven by nutrient- rich waters upwelled from depth, such that these regions are typically characterised by high rates of nitrate-fuelled phytoplankton growth. Production studies from the southern Benguela upwelling system (SBUS) tend to be biased towards the summer upwelling season, yet winter data are required to compute annual budgets and understand seasonal variability. Net primary production (NPP) and nitrate and ammonium uptake were measured concurrently at six stations in the SBUS in early winter. While euphotic zone NPP was highest at the stations nearest to the coast and declined with distance from the shore, a greater proportion was potentially exportable from open-ocean surface waters, as indicated by the higher specific nitrate uptake rates and f-ratios (ratio of nitrate uptake to total nitrogen consumption) at the stations located off the continental shelf. Near the coast, phytoplankton growth was predominantly supported by ammonium despite the high ambient nitrate concentrations. Along with ammonium concentrations as high as 3.6 µmol l^–1, this strongly suggests that nitrate uptake in the inshore SBUS, and by extension carbon drawdown, is inhibited by ammonium, at least in winter, although this has also been hypothesised for the summer.     

A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH

The transformation of irrotational surface gravity waves in an inviscid fluid can be studied by time stepping the kinematic and dynamic surface boundary conditions. This requires a closure providing the normal surface particle velocity in terms of the surface velocity potential or its tangential derivative. A convolution integral giving this closure as an explicit expression is derived for linear 1D waves over a mildly sloping bottom. The model has exact linear dispersion and shoaling properties. A discrete numerical model is developed for a spatially staggered uniform grid. The model involves a spatial derivative which is discretized by an arbitrary-order finite-difference scheme. Error control is attained by solving the discrete dispersion relation a priori and model results make a perfect match to this prediction. A procedure is developed by which the computational effort is minimized for a specific physical problem while adapting the numerical parameters under the constraint of a predefined tolerance of damping and dispersion error. Two computational examples show that accurate irregular-wave transformation on the kilometre scale can be computed in seconds. Thus, the method makes up a highly efficient basis for a forthcoming extension that includes nonlinearity at arbitrary order. The relation to Boussinesq equations, mild-slope wave equations, boundary integral equations and spectral methods is briefly discussed.     

Modern and Pleistocene boron isotope composition of the benthic foraminifer Cibicidoides wuellerstorfi

Here we present the first species-specific study of boron isotopes in the epibenthic foraminifer species Cibicidoides wuellerstorfi. Coretop samples from a water depth profile from 1000 to 4500 m on the northern flank of the Walvis Ridge are 4.4‰ lower than the values expected, based on calculations of the δ¹¹B_borate of ambient seawater. Similar values for this foraminifer species are presented from ODP site 668B at the Sierra Leone Rise, in the equatorial Atlantic. The consistency between data of the same species suggests the offsets are primary, rather than diagenetic. Glacial C. wuellerstorfi from ODP 668B and Walvis Ridge have boron isotope compositions only slightly different to interglacial samples, that is no larger than + 0.10 pH units, or + 23 µmol kg^− 1 in [CO₃²⁻] above the reconstructed glacial lysocline, and − 0.07 pH units, or − 14 µmol kg^− 1 in [CO₃²⁻] below. We use these results to suggest that glacial deep water pH in the Atlantic was similar to interglacial pH. The new data resolve the inconsistency between the previously reported high bottom water pH and the lack of significant carbonate preservation of the glacial deep ocean.     

Data reporting norms for 40Ar/39Ar geochronology

Data reported in ⁴⁰Ar/³⁹Ar geochronology studies are commonly insufficient to allow computation of ages. This deficiency renders it difficult to compare ages based on different standards or constants, and often hinders critical evaluation of the results. Herein are presented an enumeration of the data that should be reported in all ⁴⁰Ar/³⁹Ar studies, including a discussion in support of these requirements. The minimum required data are identified and distinguished from parameters that are useful but may be derived from them by calculation. Finally, recommendations are made for metadata needed to document age calculations (e.g., from age spectrum or isochron analyses).     

Evidence from Ar/Ar Ages of Individual Hornblende Grains for Varying Laurentide Sources of Iceberg Discharges 22,000 to 10,500 yr B.P.

The abundance and lithic content of ice rafted detritus in glacial North Atlantic sediment cores vary abruptly on millennial time scales that have been correlated to Dansgaard-Oeschger cycles in the Greenland ice cores. There is growing evidence that various ice sheet outlets contributed increased iceberg fluxes at multiple discrete intervals, and the relative timing of iceberg discharges from different sources is important for understanding interactions between oceans and ice sheets. We present a provenance study based on ⁴⁰Ar/³⁹Ar dates of individual hornblende grains from 20 samples taken at 600 to 700 yr spacing between 10,500 and 22,000 yr B.P., from Orphan Knoll core EW9303-GGC31. Heinrich layers are characterized by a dominant Paleoproterozoic hornblende provenance consistent with published studies. A change in provenance between Heinrich events H2 and H1 indicates contributions of iceberg calving from the Newfoundland and southern Labrador margins. Between H1 and the Younger Dryas interval, Paleoproterozoic ice rafted grains remained dominant. The dominance of Baffin Island (or Greenland?) sources to the ice rafted detritus is ascribed to the retreat of the southern Laurentide ice sheet at about the time of H1—a retreat that isolated Newfoundland and southern Labrador ice from the shelf-slope boundary.     

Second-order wavemaker theory for irregular waves

Through the last decade the theory for second-order irregular wave generation was developed within the framework of Stokes wave theory. This pioneering work, however, is not fully consistent. Furthermore, due to the extensive algebra involved, the derived transfer functions appear in an unnecessarily complicated form. The present paper develops the full second-order wavemaker theory (including superharmonics as well as subharmonics) valid for rotational as well as translatory wave board motion. The primary goal is to obtain the second-order motion of the wave paddle required in order to get a spatially homogeneous wave field correct to second order, i.e. in order to suppress spurious free-wave generation. In addition to the transfer functions developed in the line of references on which the present work is based, some new terms evolve. These are related to the first-order evanescent modes and accordingly they are significant when the wave board motion makes a poor fit to the velocity profile of the desired progressive wave component. This is, for example, the case for the high-frequency part of a primary wave spectrum when using a piston-type wavemaker. The transfer functions are given in a relatively simple form by which the computational effort is reduced substantially. This enhances the practical computation of second-order wavemaker control signals for irregular waves, and no narrow band assumption is needed. The software is conveniently included in a PC-based wave generation system—the DHI Wave Synthesizer. The validity of the theory is demonstrated for a piston type wavemaker in a number of laboratory wave experiments for regular waves, wave groups and irregular waves.     

Lithium isotopes in Guatemalan and Franciscan HP-LT rocks: Insights into the role of sediment-derived fluids during subduction

High-pressure, low-temperature (HP-LT) rocks from a Cretaceous age subduction complex occur as tectonic blocks in serpentinite mélange along the Motagua Fault (MF) in central Guatemala. Eclogite and jadeitite among these are characterized by trace element patterns with enrichments in fluid mobile elements, similar to arc lavas. Eclogite is recrystallized from MORB-like altered oceanic crust, presumably at the boundary between the down-going plate and overlying mantle wedge. Eclogite geochemistry, mineralogy and petrography suggest a two step petrogenesis of (1) dehydration during prograde metamorphism at low temperatures (<500 °C) followed by (2) partial rehydration/fertilization at even lower T during exhumation. In contrast, Guatemalan jadeitites are crystallized directly from low-T aqueous fluid as veins in serpentinizing mantle during both subduction and exhumation. The overall chemistry and mineralogy of Guatemalan eclogites are similar to those from the Franciscan Complex, California, implying similar P-T-x paths.Li concentrations (?90 ppm) in mineral separates and whole rocks (WR) from Guatemalan and Franciscan HP-LT rocks are significantly higher than MORB (4-6 ppm), but similar to HP-LT rocks globally. Li isotopic compositions range from −5‰ to +5‰ for Guatemalan HP-LT rocks, and −4‰ to +1‰ for Franciscan eclogites, overlapping previous findings for other HP-LT suites. The combination of Li concentrations greater than MORB, and Li isotopic values lighter than MORB are inconsistent with a simple dehydration model. We prefer a model in which Li systematics in Guatemalan and Franciscan eclogites reflect reequilibration with subduction fluids during exhumation. Roughly 5-10% of the Li in these fluids is derived from sediments.Model results predict that the dehydrated bulk ocean crust is isotopically lighter (δ⁷Li ? +1 ± 3‰) than the depleted mantle (∼+3.5 ± 0.5‰), while the mantle wedge beneath the arc is the isotopic complement of the bulk crust. A subduction fluid with an AOC-GLOSS composition over the full range of model temperatures (50-600 °C) gives an average fluid δ⁷Li (∼+7 ± 5‰ 1σ) that is isotopically heavier than the depleted mantle. If the lowest temperature steps are excluded (50-260 °C) as too cold to participate in circulation of the mantle wedge, then the average subduction fluid (δ⁷Li = +4 ± 2.3‰ 1σ, is indistinguishable from depleted mantle. Because of the relatively compatible nature of Li in metamorphic minerals, the most altered part of the crust (uppermost extrusives), may retain a Li isotopic signature (∼+5 ± 3‰) heavier than the bulk crust. The range of Li isotopic values for OIB, IAB and MORB overlap, making it is difficult to resolve which of these components may contribute to the recycled component in the mantle using δ⁷Li alone.