A numerical study of detached shear layers in a rotating sliced cylinder

Abstract

The low Rossby number flow in a rotating cylinder with an inclined bottom, of small slope, is examined when part of the lid of the container is rotating at a slightly different rate. The resulting flow is calculated numerically by solving the governing equations for the two-dimensional geostrophic motion which approximates the flow in most of the fluid including the inertially-modified E ^¼ -layers. The presence of ageostrophic regions, on the container walls and beneath the velocity discontinuity on the lid, is accounted for in the governing equations and their boundary conditions. This study supplements previous work on this configuration, in which the zero Rossby number flow was calculated and experimental results were presented, by enabling a direct comparison to be made between the results of the low Rossby number theory and the experiments. The numerical results for a range of Rossby and Ekman numbers compare well with those from the experiments despite a severe limitation on the size of the Rossby number arising from the analysis in the ageostrophic part of the detached shear layer.     

Marine Macrophyte Wrack Inputs and Dissolved Nutrients in Beach Sands

We investigated the role of sandy beaches in nearshore nutrient cycling by quantifying macrophyte wrack inputs and examining relationships between wrack accumulation and pore water nutrients during the summer dry season. Macrophyte inputs, primarily giant kelp Macrocystis pyrifera, exceeded 2.3 kg m⁻¹ day⁻¹. Mean wrack biomass varied 100-fold among beaches (range = 0.41 to 46.43 kg m⁻¹). Mean concentrations of dissolved inorganic nitrogen (DIN), primarily NO_x⁻-N, and dissolved organic nitrogen (DON) in intertidal pore water varied significantly among beaches (ranges = 1 to 6,553 μM and 7 to 2,006 μM, respectively). Intertidal DIN and DON concentrations were significantly correlated with wrack biomass. Surf zone concentrations of DIN were also strongly correlated with wrack biomass and with intertidal DIN, suggesting export of nutrients from re-mineralized wrack. Our results suggest beach ecosystems can process and re-mineralize substantial organic inputs and accumulate dissolved nutrients, which are subsequently available to nearshore waters and primary producers.     

Evaluation of Density Corrections to Methane Fluxes Measured by Open-Path Eddy Covariance over Contrasting Landscapes

Corrections accounting for air density fluctuations due to heat and water vapour fluxes must be applied to the measurement of eddy-covariance fluxes when using open-path sensors. Experimental tests and ecosystem observations have demonstrated the important role density corrections play in accurately quantifying carbon dioxide \((\hbox {CO}_{2})\) fluxes, but less attention has been paid to evaluating these corrections for methane \((\hbox {CH}_{4})\) fluxes. We measured \(\hbox {CH}_{4}\) fluxes with open-path sensors over a suite of sites with contrasting \(\hbox {CH}_{4}\) emissions and energy partitioning, including a pavement airfield, two negligible-flux ecosystems (drained alfalfa and pasture), and two high-flux ecosystems (flooded wetland and rice). We found that density corrections successfully re-zeroed fluxes in negligible-flux sites; however, slight overcorrection was observed above pavement. The primary impact of density corrections varied over negligible- and high-flux ecosystems. For negligible-flux sites, corrections led to greater than 100% adjustment in daily budgets, while these adjustments were only 3–10% in high-flux ecosystems. The primary impact to high-flux ecosystems was a change in flux diel patterns, which may affect the evaluation of relationships between biophysical drivers and fluxes if correction bias exists. Additionally, accounting for density effects to high-frequency \(\hbox {CH}_{4}\) fluctuations led to large differences in observed \(\hbox {CH}_{4}\) flux cospectra above negligible-flux sites, demonstrating that similar adjustments should be made before interpreting \(\hbox {CH}_{4}\) cospectra for comparable ecosystems. These results give us confidence in \(\hbox {CH}_{4}\) fluxes measured by open-path sensors, and demonstrate that density corrections play an important role in adjusting flux budgets and diel patterns across a range of ecosystems.     

The effect of net-transfer reactions on the isotopic composition of minerals

To interpret correctly the isotopic composition of metmorphic rocks and minerals, the effect of nettransfer reactions must be quantitatively evaluated. Such evaluation requires a complete set of linearly independent, net-transfer reactions that fully describe the reacting system. The set of net-transfer reactions is then coupled with mass-balance equations for stable isotopes. Reaction spaces can be contoured with isopleths of °¹⁸O, °¹³C, and D of minerals which allows evaluation of the effect of different reactions and bulk compositions on the stable isotopic composition of minerals and rocks. Using this approach, we examined the effect of fractionation of isotopes due to net-transfer reactions at the biotite and second-sillimanite isograds in northern New England. Our analysis shows that the shift in °¹³C and °¹⁸O at an isograd depends strongly upon the overall net-transfer reaction at the isograd and the bulk composition of the rock. The use of model isograd reactions to determine isotopic shifts, therefore, can lead to serious errors in the interpretation of isotopic data. At the second-sillimanite isograd °¹⁸O _qtz (quartz), °¹⁸O _kspar (K feldsdpar), and °¹⁸O _wr (whole rock) decrease by 0.5, 1.0, and 0.8 per mil, respectively. Quantitative evaluation of the effect of fractionation of isotopes by net-transfer reactions shows that: (1) the relative changes in oxygen isotopes across the isograd could be caused by distillation of fluids during develatilization reactions; (2) the magnitude of the observed isotopic shifts often differs by a factor of 2 from the calculated shifts due to reaction progress alone. The difference between observed and calculated shifts is attributed to either, differences in bulk composition between individual rocks, or, to isotopic exchange between minerals after peak metamorphism. At the biotite isograd the shifts in carbon and oxygen isotope values are different from predicted shifts caused by net-transfer reactions alone. This discrepancy suggests that fluids infiltrated the rocks during the formation of the biotite isograd.     

Ti-in-zircon thermometry: applications and limitations

The titanium concentrations of 484 zircons with U-Pb ages of ∼1 Ma to 4.4 Ga were measured by ion microprobe. Samples come from 45 different igneous rocks (365 zircons), as well as zircon megacrysts (84) from kimberlite, Early Archean detrital zircons (32), and zircon reference materials (3). Samples were chosen to represent a large range of igneous rock compositions. Most of the zircons contain less than 20 ppm Ti. Apparent temperatures for zircon crystallization were calculated using the Ti-in-zircon thermometer (Watson et al. 2006, Contrib Mineral Petrol 151:413–433) without making corrections for reduced oxide activities (e.g., TiO₂ or SiO₂), or variable pressure. Average apparent Ti-in-zircon temperatures range from 500° to 850°C, and are lower than either zircon saturation temperatures (for granitic rocks) or predicted crystallization temperatures of evolved melts (∼15% melt residue for mafic rocks). Temperatures average: 653 ± 124°C (2 standard deviations, 60 zircons) for felsic to intermediate igneous rocks, 758 ± 111°C (261 zircons) for mafic rocks, and 758 ± 98°C (84 zircons) for mantle megacrysts from kimberlite. Individually, the effects of reduced or , variable pressure, deviations from Henry’s Law, and subsolidus Ti exchange are insufficient to explain the seemingly low temperatures for zircon crystallization in igneous rocks. MELTs calculations show that mafic magmas can evolve to hydrous melts with significantly lower crystallization temperature for the last 10–15% melt residue than that of the main rock. While some magmatic zircons surely form in such late hydrous melts, low apparent temperatures are found in zircons that are included within phenocrysts or glass showing that those zircons are not from evolved residue melts. Intracrystalline variability in Ti concentration, in excess of analytical precision, is observed for nearly all zircons that were analyzed more than once. However, there is no systematic change in Ti content from core to rim, or correlation with zoning, age, U content, Th/U ratio, or concordance in U-Pb age. Thus, it is likely that other variables, in addition to temperature and , are important in controlling the Ti content of zircon. The Ti contents of igneous zircons from different rock types worldwide overlap significantly. However, on a more restricted regional scale, apparent Ti-in-zircon temperatures correlate with whole-rock SiO₂ and HfO₂ for plutonic rocks of the Sierra Nevada batholith, averaging 750°C at 50 wt.% SiO₂ and 600°C at 75 wt.%. Among felsic plutons in the Sierra, peraluminous granites average 610 ± 88°C, while metaluminous rocks average 694 ± 94°C. Detrital zircons from the Jack Hills, Western Australia with ages from 4.4 to 4.0 Ga have apparent temperatures of 717 ± 108°C, which are intermediate between values for felsic rocks and those for mafic rocks. Although some mafic zircons have higher Ti content, values for Early Archean detrital zircons from a proposed granitic provenance are similar to zircons from many mafic rocks, including anorthosites from the Adirondack Mts (709 ± 76°C). Furthermore, the Jack Hills zircon apparent Ti-temperatures are significantly higher than measured values for peraluminous granites (610 ± 88°C). Thus the Ti concentration in detrital zircons and apparent Ti-in-zircon temperatures are not sufficient to independently identify parent melt composition. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Implications of uncertain future fossil energy resources on bioenergy use and terrestrial carbon emissions

The magnitude and character of the global resource base of fossil fuels is a key determinant of the evolution of the future global energy system and corresponding fossil fuel carbon emissions. What is less well understood is the potential magnitude of impact of the availability of fossil fuels, due to the interaction with biomass energy, on agriculture, land use, ecosystems and therefore carbon emissions from land-use change. This paper explores these links and implications. We show that if oil resources are limited, then the consequently higher price for liquids induces both the use of coal-to-liquids technology deployment, but also enhanced production of bioenergy crops particularly in a business-as-usual scenario. This in turn implies greater pressure to convert unmanaged ecosystems to produce bioenergy, and higher rates of terrestrial carbon emissions from land use.