Numerical solution of the dispersion equation using a variable dispersion coefficient: method and applications

ABSTRACT

The study presented herein forms part of a wider research project on dispersion prediction in open channel flows which include laboratory, field and numerical investigations. In this paper, a numerical model which uses finite elements in space and finite differences in time for the solution of the convective-dispersion equation is developed and verified. In the model, the dispersion coefficient is considered as a function of time (or distance) during the initial period. It is represented by a modified Fickian type model which has been calibrated by the authors using laboratory data. The numerical model has been used to predict concentration profiles of tracer studies carried out in the laboratory as well as in the field.     

Barium-rich fluids and melts in a subduction environment (La Corea and Sierra del Convento mélanges,eastern Cuba)

Whole-rock compositions of muscovite-bearing amphibolite, trondhjemite, pegmatite and quartz-muscovite rocks from Sierra del Convento and La Corea mélanges (eastern Cuba), as well as mineralogy, record complex circulation of Ba-rich fluids and melts in the subduction environment. Partial melting of fluid-fluxed, MORB-derived amphibolite produced trondhjemite magmas that crystallized at depth, in some cases evolving into pegmatites. Qtz-Ms rocks probably crystallized from primary fluids derived from subducted sediments. All these rocks have elevated concentrations of large-ion lithophile elements, especially Ba (up to 11,810 ppm), presumably released from slab sediments by fluids and/or melts. Fluid–rock interaction produced crystallization of phengite in parental amphibolites. The phengite crystallized in all types of rocks is rich in Ba, with concentric zoning, characterized by Ba-rich cores and Ba-poor rims, indicating a compatible behaviour of Ba in the studied systems. Zoning in phengite is governed primarily by the celadonite (tschermak) exchange vector ((Mg,Fe)Si-(Al)_-2), with more moderate contributions of the celsian (BaAl-(KSi)_-1) and paragonite (NaK_-1) exchange vectors. Late remobilization of Ba at relatively low temperature formed retrograde celsian. The compatible behaviour of Ba in the studied rocks strengthens the importance of the stability of phengite for the transfer of LIL elements from the subduction to the volcanic arc environments.     

Lateral structural variability in zone of eocene island-arc-continent collision,Kamchatka

The lateral variability of structural elements in the collision zone of the Cretaceous-Paleocene Achaivayam-Valagin island arc with the northeastern Asian margin is considered. The similarity and difference of Eocene collision structural elements in the north and the south of Kamchatka are shown. In northern Kamchatka, the continent-arc boundary is traced along the Lesnaya-Vatyn Thrust Fault, which completed its evolution about 45 Ma ago. The thin, near-horizontal allochthon of this thrust, composed of island-arc rocks, overlies the deformed but unmetamorphosed terrigeneous sequences of the Asian margin. The general structure of this suture in the Kamchatka Isthmus and southern Koryakia is comparable with the uppermost subduction zone, where a thin lithospheric wedge overlaps intensely deformed sediments detached from the plunging plate. In southern Kamchatka (Malka Uplift of the Sredinny Range), the arc-continent collision started 55–53 Ma ago with thrusting of island-arc complexes over terrigenous rocks of continental margin. However, the thickness of the allochthon was much greater than in the north. Immediately after this event, both the autochthon and lower part of allochthon were deformed and subsided to a significant depth. This subsidence gave rise to metamorphism of both the autochthon (Kolpakov and Kamchatka groups, Kheivan Formation) and lower allochthon (Andrianovka and Khimka formations). The anomalously fast heating of the crust was most likely related to the ascent of asthenospheric masses due to slab breakoff, when the Eurasian Plate was plunging beneath the Achaivayam-Valagin arc.     

The anatomy of Continental Flood Basalt Provinces: geological constraints on the processes and products of flood volcanism

The internal architecture of the immense volumes of eruptive products in Continental Flood Basalt Provinces (CFBPs) provides vital clues, through the constraint of a chrono-stratigraphic framework, to the origins of major intraplate melting events. This work presents close examination of the internal facies architecture and structure, duration of volcanism, epeirogenetic uplift associated with CFBPs, and the potential environmental impacts of three intensely studied CFBPs (the Parana-Etendeka, Deccan Traps and North Atlantic Igneous Province). Such a combination of key volcanological, stratigraphic and chronologic observations can reveal how a CFBP is constructed spatially and temporally to provide crucial geological constraints regarding their development.

Using this approach, a typical model can be generated, on the basis of the three selected CFBPs, that describes three main phases of flood basalt volcanism. These phases are recognized in Phanerozoic CFBPs globally. At the inception of CFBP volcanism, relatively low-volume transitional-alkaline eruptions are forcibly erupted into exposed cratonic basement lithologies, sediments, and in some cases, water. Distribution of initial volcanism is strongly controlled by the arrangement of pre-existing topography, the presence of water bodies and local sedimentary systems, but is primarily controlled by existing lithospheric and crustal weaknesses and concurrent regional stress patterns. The main phase of volcanism is typically characterised by a culmination of repeated episodes of large volume tholeiitic flows that predominantly generate large tabular flows and flow fields from a number of spatially restricted eruption sites and fissures. These tabular flows build a thick lava flow stratigraphy in a relatively short period of time (c. 1–5 Ma). With the overall duration of flood volcanism lasting 5–10 Ma (the main phase accounting for less than half the overall eruptive time in each specific case). This main phase or ‘acme’ of volcanism accounts for much of the CFBP eruptive volume, indicating that eruption rates are extremely variable over the whole duration of the CFBP. During the waning phase of flood volcanism, the volume of eruptions rapidly decrease and more widely distributed localised centres of eruption begin to develop. These late-stage eruptions are commonly associated with increasing silica content and highly explosive eruptive products. Posteruptive modification is characterised by continued episodes of regional uplift, associated erosion, and often the persistence of a lower-volume mantle melting anomaly in the offshore parts of those CFBPs at volcanic rifted margins.     

Paleomagnetism of the triassic nicola volcanics and geotectonics of the quesnellia subterrane of terrane I, British Columbia

Paleomagnetic data from 46 sites (674 specimens) of the Westcoast Crystalline Gneiss Complex on the west coast of Vancouver Island using AF and thermal demagnetization methods yields a high blocking temperature WCB component (> 560°C) with a pole at 335°W, 66°N (δ_p = 4°, δ_m = 6°) and a lower coercivity WCA component ( 25 mT, < 500°C) with a pole at 52°W, 79°N (δ_p = 7°, δ_m = 8°). Further thermal demagnetization data from 24 sites in the Jurassic Island Intrusions also defines two high blocking temperature components. The IIA component pole is at 59°W, 79°N (δ_p = 7°, δ_m = 8°) and IIB pole at 130°W, 73°N (δ_p = 12°, δ_m = 13°). Combined with previous data from the Karmutsen Basalts and mid-Tertiary units on Vancouver Island and from the adjacent Coast Plutonic Complex, the geotectonic motions are examined for the Vancouver Island segment of the Wrangellian Subterrane of composite Terrane II of the Cordillera. The simplest hypothesis invokes relatively uniform translation for Terrane II from Upper Triassic to Eocene time producing 39° ± 6° of northward motion relative to the North American craton, combined with 40° of clockwise rotation during the Lower Tertiary.     

Characterizing the severe turbulence environments associated with commercial aviation accidents. A real-time turbulence model (RTTM) designed for the operational prediction of hazardous aviation turbulence environments

Summary In this paper, we will focus on the real-time prediction of environments that are predisposed to producing moderate-severe (hazardous) aviation turbulence. We will describe the numerical model and its postprocessing system that is designed for said prediction of environments predisposed to severe aviation turbulence as well as presenting numerous examples of its utility. The purpose of this paper is to demonstrate that simple hydrostatic precursor circulations organize regions of preferred wave breaking and turbulence at the nonhydrostatic scales of motion. This will be demonstrated with a hydrostatic numerical modeling system, which can be run in real time on a very inexpensive university computer workstation employing simple forecast indices. The forecast system is designed to efficiently support forecasters who are directing research aircraft to measure the environment immediately surrounding turbulence. The numerical model is MASS version 5.13, which is integrated over three different grid matrices in real-time on a university workstation in support of NASA-Langley’s B-757 turbulence research flight missions. The model horizontal resolutions are 60, 30, and 15 km and the grids are centered over the region of operational NASA-Langley B-757 turbulence flight missions. The postprocessing system includes several turbulence-related products including four turbulence forecasting indices, winds, streamlines, turbulence kinetic energy, and Richardson numbers. Additionally there are convective products including precipitation, cloud height, cloud mass fluxes, lifted index, and K-index. Furthermore, soundings, sounding parameters, and Froude number plots are also provided. The horizontal cross section plot products are provided from 16,000–46,000 feet in 2,000 feet intervals. Products are available every three hours at the 60 and 30 km grid interval and every 1.5 hours at the 15 km grid interval. The model is initialized from the NWS ETA analyses and integrated two times a day.     

Using δ<Superscript>18</Superscript>O as a Tracer of the Formation of Water Masses in the Laptev Sea. Part 1. Quantification of Ice Formation and Melting

Data on salinity and δ¹⁸O from the NASA open-source database are used to estimate the Laptev Sea water mass transformation during ice formation and melting. The indicator of these processes is salinity variation. The estimates for the Laptev Sea show that the amount of meltwater can reach 40% for the sea water with salinity below 7 psu. In this case, sea water salinity reduction due to the meltwater inflow alone can be equal to 0.2-0.7 psu. In the sea water with salinity above 7 psu, ice formation prevails over ice melting. This process is the most strongly pronounced in the range of sea water salinity from 15 to 25 psu. In this salinity range, the average water removal for the ice formation makes up 9% (the maximum is 24%), and the average salinity growth is 0.5 psu (the maximum is 1.7 psu). The most transformed sea water masses during ice formation are located in the bottom layer of the shallow southern and southeastern parts of the Laptev Sea, where the sea depth is not more than 50 m.     

Role of land-surface temperature feedback on model performance for the stable boundary layer

At present a variety of boundary-layer schemes is in use in numerical models and often a large variation of model results is found. This is clear from model intercomparisons, such as organized within the GEWEX Atmospheric Boundary Layer Study (GABLS). In this paper we analyze how the specification of the land-surface temperature affects the results of a boundary-layer scheme, in particular for stable conditions. As such we use a well established column model of the boundary layer and we vary relevant parameters in the turbulence scheme for stable conditions. By doing so, we can reproduce the outcome for a variety of boundary-layer models. This is illustrated with the original set-up of the second GABLS intercomparison study using prescribed geostrophic winds and land-surface temperatures as inspired by (but not identical to) observations of CASES-99 for a period of more than two diurnal cycles. The model runs are repeated using a surface temperature that is calculated with a simple land-surface scheme. In the latter case, it is found that the range of model results in stable conditions is reduced for the sensible heat fluxes, and the profiles of potential temperature and wind speed. However, in the latter case the modelled surface temperatures are rather different than with the original set-up, which also impacts on near-surface air temperature and wind speed. As such it appears that the model results in stable conditions are strongly influenced by non-linear feedbacks in which the magnitude of the geostrophic wind speed and the related land-surface temperature play an important role.     

Ore lead and sulphur isotope pattern from the low-temperature veins of the Catalonian Coastal Ranges (NE Spain)

The lead isotopic composition of galenas from low-temperature veins of the Catalonian Coastal Ranges (NE Spain) displays a small but distinct range of values: 18.318 ≤²⁰⁶Pb/²⁰⁴Pb ≤ 18.678; 15.678 ≤²⁰⁷Pb/²⁰⁴Pb ≤ 15.767 and 38.534 ≤ ²⁰⁸Pb/²⁰⁴Pb ≤ 39.189. The data define a linear trend in the ²⁰⁸Pb/²⁰⁴Pb versus ²⁰⁶Pb/²⁰⁴Pb diagram that can be interpreted in terms of mixing of lead from different reservoirs. The lead appears to be derived from a solution that preferentially leached granites of Late-Hercynian age. Sulphur isotopic compositions of the galenas range from −8.5 to + 7.3‰ but variations in a single deposit are small (1–2‰), pointing to different sources of sulphur. In a δ³⁴S versus ²⁰⁶Pb/²⁰⁴Pb plot no clear correlation trends appear. Lead isotope data from deposits of similar characteristics situated within the Hercynian orogenic belt as the Linares-La Carolina district (S Spain) and the Inglesiente-Sulcis area (Sardinia) show slight differences indicating a source area of similar lead isotopic composition. In the CCR and Linares-La Carolina districts, the main source of lead is related to the Hercynian granites of each area, although small contributions from metasediments cannot be ruled out. The contribution of lead from metasedimentary rocks is particularly seen in the Sardinian (Hercynian vein-type) ores. Received: 8 August 1996 / Accepted: 5 December 1996     

Evolution of Miocene fluvial environments, eastern Potwar plateau, northern Pakistan

The Miocene-Pliocene Siwalik Group records changing fluvial environments in the Himalayan foreland basin. The Nagri and Dhok Pathan Formations of this Group in the eastern Potwar Plateau, northern Pakistan, comprise relatively thick (tens of metres) sandstone bodies and mudstones that contain thinner sandstone bodies (metres thick) and palaeosols. Thick sandstone bodies extend for kilometres normal to palaeoflow, and are composed of large-scale stratasets (storeys) stacked laterally and vertically adjacent to each other. Sandstone bodies represent single or superimposed braided-channel belts, and large-scale stratasets represent channel bars and fills. Channel belts had widths of km, bankfull discharges on the order of 10³ cumecs and braiding parameter up to about 3. Individual channel segments had bankfull widths, maximum depths, and slopes on the order of 10² m, 10¹ m and 10^?4 respectively, and sinuosities around 1-1. These rivers are comparable to many of those flowing over the megafans of the modern Indo-Gangetic basin, and a similar depositional setting is likely. Thin sandstone bodies within mudstone sequences extend laterally for on the order of 10² m and have lobe, wedge, sheet and channel-form geometries: they represent crevasse splays, levees and floodplain channels. Mudstones are relatively bioturbated/disrupted and represent mainly floodbasin and lacustrine deposition. Mudstones and sandstones are extremely disrupted in places, showing evidence of prolonged pedogenesis. These ‘mature’ palaeosols are m thick and extend laterally for km. Lateral and vertical variations in the nature of their horizons apparently depend mainly on deposition rate. The 500 m-thick Nagri Formation has a greater proportion and thicker sandstone bodies than the overlying 700 m-thick Dhok Pathan Formation. The thick sandstone bodies and their large-scale stratasets thicken and coarsen through the Nagri Formation, then thin and fine at the base of the Dhok Pathan Formation. Compacted deposition rates increase with sandstone proportion (0-53 mm/year for Nagri, 0-24 mm/year for Dhok Pathan), and palaeosols are not as well developed where deposition rates are high. Within both formations there are 100 m-scale variations (representing on the order of 10⁵ years) in the proportion and thickness of thick sandstone bodies, and tens-of-m-scale alternations of thick sandstone bodies and mudstone-sandstone strata that represent on the order of 10⁴ years. Formation-scale stratal variations extend across the Potwar Plateau for at least 100 km, although they may be diachronous: however, 100-m and smaller scale variations can only be traced laterally for up to tens of km. Alluvial architecture models indicate that increases in the proportion and thickness of thick sandstone bodies can be explained by increasing channel-belt sizes (mainly), average deposition rate and avulsion frequency on a megafan comparable in size to modern examples. 100-m-scale variations in thick sandstone-body proportion and thickness could result from ‘regional’ shifts in the position of major channels, possibly associated with ‘fan lobes’on a single megafan or with separate megafans. However, such variations could also be related to local changes in subsidence rate or changes in sediment supply to the megafan system. Formation-scale and 100-m-scale stratal variations are probably associated with interelated changes in tectonic uplift, sediment supply and basin subsidence. Increased rates of hinterland uplift, sediment supply and basin subsidence, recorded by the Nagri Formation, may have resulted in diversion of a relatively large river to the area. Alternatively, changing river sizes and sediment supply rates may be related to climate changes affecting the hinterland (possibly linked to tectonic uplift). Climate during deposition of the Siwalik Group was monsoonal. Although the deposits contain no direct evidence for climate change, independent evidence indicates global cooling throughout the Miocene, and the possibility of glacial periods (e.g. around 10-8 Ma, corresponding to base of Nagri Formation). If the higher Himalayas were periodically glaciated, a mechanism would exist for varying sediment supply to megafans on time scales of 10⁴-10⁵ years. Although eustatic sea-level changes are related to global climatic change, they are not directly related to Siwalik stratigraphic changes, because the shoreline was many 100 km away during the Miocene.