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.     

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.     

Sediment sources of northern Québec and Labrador glacial deposits and the northeastern sector of the Laurentide Ice Sheet during ice-rafting events of the last glacial cycle

Provenance studies of anomalously high-flux layers of ice-rafted detritus (IRD) in North Atlantic sediments of the last glacial cycle show evidence for massive iceberg discharges coming from the Hudson Strait region of the Laurentide Ice Sheet (LIS). Although these so-called Heinrich events (H events) are commonly thought to be associated with abrupt drawdown of the LIS interior, uncertainties remain regarding the sector(s) of this multi-domed ice sheet that conveyed ice through Hudson Strait. In Northern Québec and Labrador (NQL), large-scale patterns of glacial lineations indicate massive ice flows towards Ungava Bay and Hudson Strait that could reflect the participation of the Labrador–Québec ice dome in H events. Here we evaluate this hypothesis by constraining the source of NQL glacial deposits, which provide an estimate of the provenance characteristics of IRD originating from this sector. Specifically, we use ⁴⁰Ar/³⁹Ar ages of detrital hornblende grains in 25 till samples distributed along a latitudinal transect (lat. 58°) extending east and west of Ungava Bay. The data show that tills located west and southwest of the Ungava Bay region are largely dominated by hornblende grains with Archean ages (>2.6 Ga), while tills located east of Ungava Bay are characterized by grains with early Paleoproterozoic ages (2.0–1.8 Ga), although most samples contain a few Archean-age grains. IRD derived from the NQL region should thus be characterized by a large proportion of Archean-age detrital grains, which contrasts significantly with the predominant Paleoproterozoic ⁴⁰Ar/³⁹Ar ages (1.8–1.6 Ga) typically reported for the dominant age population of hornblende grains in H layers. Comparisons with IRD through the last glacial cycle from a western North Atlantic core off Newfoundland do not show evidence for any prominent ice-rafted event with the provenance characteristics of NQL glacial deposits, thereby suggesting that significant ice-calving event(s) from the Labrador–Québec sector may have been limited throughout that interval. Although these results tend to point towards a relative stability of this ice dome during H events, our study also indicates that further provenance work is required on IRD proximal to the Hudson Strait mouth in order to constrain with a greater confidence the sector(s) of the LIS that fed ice into Hudson Strait during H events. Alternatively, these results and other paleogeographic considerations tend to support models suggesting that part of the Ungava Bay glacial lineations could be associated with a Late-Glacial ice flow across Hudson Strait.     

Contrasting conditions preceding MIS3 and MIS2 Heinrich events

This paper presents an integrated multi-tracer study performed on piston cores recovered in the glacial ice-rafted detritus belt, stretching from Newfoundland to the Irish margin across the North Atlantic (40–55°N), in order to compare in detail the internal structure of each Heinrich event (HE). These tracers are IRD counts (quartz, dolomite, volcanic grains), their Nd isotopic composition and Ar–Ar datings of individual hornblende grains. A focus on the detailed structure of HE confirms that all intervals of massive sediment flux, specifically Heinrich layers HL1-to-5 (HLs), were dominated by North American, Laurentide ice-sheet surges from Hudson Strait, that are evident as far east as the Bay of Biscay (European margin). The sequences of events leading up to the HLs, however, present significant dissimilarities. One important difference is that HL2 and HL1 were preceded by “precursor events” (increases in the number of lithic grains per gram from non-Laurentide sediment sources). Sediment debris derived from near-simultaneous iceberg releases originating from the European ice-sheet are only detectable close to the European margin. In contrast there are no comparable precursor events before HL5 and HL4. This observation implies that precursor events are unlikely to be mechanistically linked to the triggering of HEs. The similarity of the HLs, against contrasting background conditions, is a significant observation that should add constraints to their origin.