Comparison of Dirichlet–Neumann operator expansions for nonlinear surface gravity waves

The Dirichlet–Neumann operator for the water-wave problem was introduced and expanded by Craig and Sulem [Craig, W., Sulem, C., 1993. [CS] Numerical simulation of gravity waves. J. Comput. Phys. 108, 73–83] and in a slightly different form and for 3D waves by Bateman, Swan and Taylor [Bateman, W.J.D., Swan, C., Taylor, P.H., 2001. [BST] On the efficient numerical simulation of directionally spread surface water waves. J. Comput. Phys. 174, 277–305]. This approach is supposedly superior to techniques derived earlier by West et al. [West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., Milton, R.L., 1987. [WW] A new numerical method for surface hydrodynamics. J. Geophys. Res. 92 (C11), 11803–11824] and Dommermuth and Yue [Dommermuth, D.G., Yue, D.K.P., 1987. [DY] A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288] under seemingly more restrictive assumptions. This paper extracts the Dirichlet–Neumann operator expansions from West et al. and Dommermuth and Yue. Concerning the operator expansions alone it is found that Bateman et al. is identical to West et al. and Dommermuth and Yue while Craig and Sulem is slightly different due to minor differences in the operator definition. For application to the free-surface boundary conditions West et al. devised a consistent truncation at nonlinear order. This alters the equivalence of the different approaches when it comes to the evaluation of the temporal derivative of the free surface elevation, which is decisive for wave evolution. In this regard Craig and Sulem is found to be identical to West et al. while Bateman et al. is identical to Dommermuth and Yue. Pseudo code is provided for alternative computational schemes in Fourier-space and physical space, respectively, along with a discussion of efficiency and potential flexibility.     

内蒙古鸡冠山斑岩钼矿床成矿时代和成矿流体研究

内蒙古鸡冠山钼矿床是西拉沐伦钼成矿带上的典型斑岩矿床。矿床产于火山侵入杂岩中,矿化类型以细脉浸染状矿化为主。对矿床5件辉钼矿样品进行了铼-锇同位素分析,获得了151.1±1.3Ma的等时线年龄,表明成矿作用发生在晚侏罗世。成矿作用可划分为三个阶段:早阶段为石英-黄铁矿阶段,发育乳白色石英和粗粒浸染状黄铁矿;中阶段包括早期石英-多金属硫化物亚阶段和晚期石英-萤石-金属硫化物亚阶段;晚阶段为石英-碳酸盐细脉,穿切早、中阶段脉体和矿物组合。鸡冠山钼矿床流体包裹体岩相学研究表明,与成矿有关的包裹体主要有六种类型:富液相、富气相、含子晶多相、含CO2三相、纯CO2及纯液相包裹体。其中,早阶段以富气和富CO2包裹体为主,中阶段多种包裹体共存,晚阶段则主要为富液包裹体。冷热台显微测温和激光拉曼显微探针(LRM)成分分析结果表明,早阶段石英中原生包裹体的均一温度480℃,盐度最高66.75%NaCleqv,包裹体气相成分富含水和CO2,液相成分则以水为主,子晶矿物有石盐、黄铜矿以及指示氧化条件的赤铁矿等,同时也说明成矿流体是富含成矿金属元素的。中阶段早期石英中的流体包裹体均一温度为320～480℃,晚期石英和萤石中的流体包裹体的均一温度为180～320℃。中阶段流体盐度介于4.65%～56.76%NaCleqv。中阶段包裹体含石盐、方解石、黄铜矿、赤铁矿等子矿物,富气相、富液相与含子晶多相包裹体共存,且具有相近的均一温度,而盐度相差悬殊,指示流体发生了沸腾。晚阶段流体的温度降低至100～180℃,盐度则低于10.86%NaCleqv,流体包裹体成分主要为水。鸡冠山钼矿成矿流体演化从早至晚为:从早阶段高温、高盐度、高氧逸度、富CO2、富成矿物质以岩浆热液为主成矿流体,演化至晚期低温、低盐度、无子晶、贫CO2、以大气降水为主的流体。沸腾作用是鸡冠山钼矿形成的重要机制。     

Self-generated aperiodic behaviour in a simple climate model

Climatic variability arising from the coupling between ocean temperature and sea-ice extent is studied in a spatially distributed system. A spatial degree of freedom is crudely introduced by the coupling, through energy transfer, of two box models each of which describes a different space region. The evolution equations are cast into a normal form and some qualitative features of this general class of models are predicted. It is shown, both analytically and numerically, that internally generated complexity in the form of aperiodic behaviour can be a natural consequence of spatially distributed systems.     

Assessing Li and other leachable geochemical proxies for paleo-salinity in lake sediments from the Mono Basin, CA (USA)

Regional climate-driven hydrological changes are accompanied by salinity changes in closed basin lakes. We have investigated acid leachable Li, along with other leachable ions including Mg, Ca and Sr, as geochemical proxies of salinity in lake sediments in the Mono Basin, California. All the elements in the acid leachable suite show a strong correlation with paleo-lake level estimates based on physical and stratigraphic evidence. The CaCO₃ content of lake sediments, which has been shown to be a reliable proxy for lake level changes in the Mono basin and the adjoining Owens Lake basin, corresponds well with our acid-leachable proxy data.     

松辽盆地徐家围子营城组流纹岩地球化学特征及构造指示意义

松辽盆地徐家围子营城组发育一套以流纹岩为主的中酸性火山岩。岩石薄片观察和主量、微量元素研究发现,后期热液蚀变、区域埋深及低温水合作用对流纹岩的Si、K、Rb等元素含量产生一定影响; 流纹岩明显富集Rb、Th、U、Pb等强不相容元素,Ba、Sr、Ti、Eu、P 负异常,暗示其经历了斜长石、磷灰石和钛铁矿分离结晶作用。流纹岩的(⁸⁷Sr/⁸⁶Sr)_i(0.705265 ~ 0.711895)值变化范围较大,大多数ε_Nd(t)为正值(1.83 ~ 3.38),Pb同位素比值相对集中,(²⁰⁶Pb/²⁰⁴Pb)_i=18.09～18.32,(²⁰⁷Pb/²⁰⁴Pb)_i=15.50 ~ 15.54,(²⁰⁸Pb/²⁰⁴Pb)_i=37.80 ~ 38.10。研究表明,岩石的源区为大比例年轻成分与少量古老地壳的混合部分熔融,其演化过程中经历了不同程度的地壳混染。松辽盆地早白垩世火山岩为板内伸展环境喷发的产物,可能与太平洋板块俯冲导致的中国东部岩石圈减薄、软流圈上涌密切相关。     

Comment on “A critical evaluation of the boron isotope-pH proxy: The accuracy of ancient ocean pH estimates” by M. Pagani, D. Lemarchand, A. Spivack and J. Gaillardet

Pagani et al. [Pagani M., Lemarchand D., Spivack A., and Gaillardet J. (2005). A critical evaluation of the boron isotope-pH proxy: the accuracy of ancient ocean pH estimates. Geochim. Cosmochim. Acta69(4), 953-961] use data from previous boron isotope studies to suggest that the fractionation between boric acid and borate in seawater as well as the history of δ¹¹B in seawater are poorly understood, thus limiting our ability to capture realistic ocean pH with this proxy. Although we agree with the authors that the long recognized uncertainty in the secular variation of δ¹¹B_seawater imposes a temporal limit on paleo-pH reconstructions, their evaluation of the δ¹¹B/pH relationship in carbonates is flawed. Potential complications from vital, temperature and dissolution effects reported in that paper are based on studies that are experimentally and/or analytically poorly constrained. Using published validation studies we will demonstrate that many of the problems outlined by Pagani et al. have already been addressed, or are based on misinterpretations of previous work. Most importantly, statistical evaluation suggests empirical data are best described by a fractionation of ∼20‰. Recent paleoreconstructions confirm that the boron isotope proxy can be used with confidence, if sample selection and analyses are done carefully.     

The lithium isotopic composition of waters of the Mono Basin, California

Mono Lake, a major closed-basin alkaline salt lake in eastern California, derives its water from a mixture of creeks and springs, with the former providing in excess of 75% of the total. The Li isotopic composition of lake water has not varied significantly over a 4 year meromictic period (δ⁷Li ∼ +19.5). Springs are isotopically distinct: groundwater springs and seeps carry water enriched in isotopically heavy Li whereas thermal springs supply isotopically light (δ⁷Li < lake), but 10 times more Li-rich, water. Isotopic fractionation during crystallization of carbonate tufa and evaporitic salt appears to be insignificant, and thus cannot be called on as a principal control of the isotopic balance of Li of the lake. Isotopic differences between the end-member source components permit a water budget to be calculated, suggesting (1) springs provide > 50% of the Li to the lake; (2) the Li budget is sensitively balanced on small thermal spring contributions, < 3% of the total spring inflow; and (3) the residence time of Li in the lake is 28 ka. Other Great Basin closed lakes have variable Li isotopic compositions (δ⁷Li from +16.7 to +23.7), all of which differ significantly from those of several major lakes and seawater (homogeneously ∼ +32).     

Effects of calcium and magnesium on strontium distribution coefficients

 The effects of calcium and magnesium on the distribution of strontium between a surficial sediment and simulated wastewater solutions were measured as part of an investigation to determine strontium transport properties of surficial sediment at the Idaho National Engineering Laboratory (INEL), Idaho. The investigation was conducted by the U.S. Geological Survey and Idaho State University, in cooperation with the U.S. Department of Energy. Batch experimental techniques were used to determine strontium linear sorption isotherms and distribution coefficients (K _d's) using simulated wastewater solutions prepared at pH 8.0±0.1 with variable concentrations of calcium and magnesium. Strontium linear sorption isotherm K _d's ranged from 12±1 to 85±3 ml/g, increasing as the concentration of calcium and magnesium decreased. The concentration of sorbed strontium and the percentage of strontium retained by the sediment were correlated to aqueous concentrations of strontium, calcium, and magnesium. The effect of these cation concentrations on strontium sorption was quantified using multivariate least-squares regression techniques. Analysis of data from these experiments indicates that increased concentrations of calcium and magnesium in wastewater discharged to waste disposal ponds at the INEL increases the availability of strontium for transport beneath the ponds by decreasing strontium sorption to the surficial sediment. Received: 8 November 1996 · Accepted: 6 January 1997     

Freshwater control of ice-rafted debris in the last glacial period at Mono Lake, California, USA

The type section silts of the late Pleistocene Wilson Creek Formation at Mono Lake contain outsized clasts, dominantly well-rounded pebbles and cobbles of Sierran lithologies. Lithic grains > 425 μm show a similar pattern of variability as the > 10 mm clasts visible in the type section, with decreasing absolute abundance in southern and eastern outcrops. The largest concentrations of ice-rafted debris (IRD) occur at 67–57 ka and 46–32 ka, with strong millennial-scale variability, while little IRD is found during the last glacial maximum and deglaciation.Stratigraphic evidence for high lake level during high IRD intervals, and a lack of geomorphic evidence for coincidence of lake and glaciers, strongly suggests that rafting was by shore ice rather than icebergs. Correspondence of carbonate flux and IRD implies that both were mainly controlled by freshwater input, rather than disparate non-climatic controls. Conversely, the lack of IRD during the last glacial maximum and deglacial highstands may relate to secondary controls such as perennial ice cover or sediment supply. High IRD at Mono Lake corresponds to low glacial flour flux in Owens Lake, both correlative to high warm-season insolation. High-resolution, extra-basinal correlation of the millennial peaks awaits greatly improved age models for both records.