Free surface flow of an incompressible fluid over a shallow plane/undulating horizontal bed is characteristically turbulent due to disturbances generated by the bed resistance and other causes. The governing equations of such flows in one dimension, for finite amplitude of surface elevation over the bed, are the Continuity Equation and a highly nonlinear Momentum Equation of order three. The method developed in this paper introduces the “discharge” variable q = ηU, where η = elevation of the free surface above the bed level, and U = average stream-wise forward velocity. By this substitution, the continuity equation becomes a linear first-order PDE and the momentum equation is transformed after introduction of a small approximation in the fifth term. Next, it is shown by an invertibility argument that q can be a function of η: q = F(η), rendering the momentum equation as a first order, second degree ODE for F(η), that can be be integrated by the Runge-Kutta method. The continuity equation then takes the form of a first order evolutionary PDE that can be integrated by a Lax-Wendroff type of scheme for the temporal evolution of the surface elevation η. The method is implemented for two particular cases: when the initial elevation is triangular with vertical angle of 120 ° and when it has a sinusoidal form. The computations exhibit the physically interesting feature that the frontal portion of the propagating wave undergoes a sharp jump followed by tumbling over as a breaker. Compared to other discretization methods, the application of the Runge-Kutta and an extended version of the Lax-Wendroff scheme is much easier. 相似文献
The present study deals with the preparation of a landslide susceptibility map of the Balason River basin, Darjeeling Himalaya, using a logistic regression model based on Geographic Information System and Remote Sensing. The landslide inventory map was prepared with a total of 295 landslide locations extracted from various satellite images and intensive field survey. Topographical maps, satellite images, geological, geomorphological, soil, rainfall and seismic data were collected, processed and constructed into a spatial database in a GIS environment. The chosen landslide-conditioning factors were altitude, slope aspect, slope angle, slope curvature, geology, geomorphology, soil, land use/land cover, normalised differential vegetation index, drainage density, lineament number density, distance from lineament, distance to drainage, stream power index, topographic wetted index, rainfall and peak ground acceleration. The produced landslide susceptibility map satisfied the decision rules and ?2 Log likelihood, Cox &; Snell R-Square and Nagelkerke R-Square values proved that all the independent variables were statistically significant. The receiver operating characteristic curve showed that the prediction accuracy of the landslide probability map was 96.10%. The proposed LR method can be used in other hazard/disaster studies and decision-making. 相似文献
Trace-element geochemistry of sandstones are being used to determine provenance. We have conducted preliminary and limited experiments to determine to what extent daughter sands retain the geochemical signature of parent rocks. Six sets of first-order stream sediments, soils from adjacent slopes, and a variety of parent rocks were collected from southwestern Montana, U.S.A. Sampling in a low-relief area ensured that climate and residence time of soils on slopes could be eliminated as variables. Sand-size fractions of stream sediments and soils, and the corresponding parent rocks (granodiorite, quartz monzonite, granite gneiss, biotite-tonalite gneiss and amphibolite) were analyzed for most major elements and selected trace elements. Petrologic modal analysis of the parent rocks and the 0.25–0.50-mm fraction of each sand was done to monitor major mineralogic control, if any, on chemical compositions of the samples.
Our data show that the abundances of the Si and Al in sediments do not discriminate provenance. Abundances of Ca, Mg, Fe and Ti may broadly distinguish between sands derived from metamorphic and igneous source rocks, at least in the area studied. Differences in abundances of the Ba and Th, and the ratio of La/Lu between granitic, tonalitic and amphibolitic parent rocks are preserved in the daughter sediments that we studied. However, the size of the Eu anomaly in the REE patterns of different daughter sediments is not diagnostic of parent rocks. Abundances of Co and Sc distinguish between sediments derived from felsic and mafic rocks. A better provenance discrimination is obtained if the ratios La/Sc, Th/Sc, La/Co, Ba/Sc and Ba/Co are used.
Petrologic modal data show that mineral contents and chemical compositions of parent rocks are compatible with each other. The chemical composition of the sands may be roughly correlated to the petrological modal data but the abundances of some minor and trace elements of sediments cannot be inferred from modal mineralogy. This is expected because these elements may concentrate in accessory minerals and/or may weather out into aqueous or clay mineral fractions; it is also compatible with conclusions of previous studies that some of these elements do not reside in sand-size fractions of siliciclastic sediments. 相似文献
Wudalianchi volcanic rocks are the most typical Cenozoic potassic volcanic rocks in easten China.Compositional comparisons between whole rocks and glasses of various occurrences indicate that the magma tends to become rich in silica and alkalis as a result of crystal differentiation in the course of evolu-tion.They are unique in isotopic composition with more radiogenic Sr but less radiogenic Pb.^87Sr/^86Sr is higher and ^143Nd/^144Nd is lower than the undifferentiated global values.In comparison to continental pot-ash volcanic rocks,Pb isotopes are apparently lower.These various threads of evidence indicate that the rocks were derived from a primary enriched mantle which had not been subjected to reworking and shows no sign of incorporation of crustal material.The correlation between Pb and Sr suggests the regional heterogeneity in the upper mantle in terms of chemical composition. 相似文献
Helium, Sr, and Nd isotopic ratios and major and trace element compositions have been measured on a suite of lavas from the intra-plate volcanos of the Juan Fernandez Archipelago, Chile. Lavas from the islands of Mas Afuera and Mas a Tierra and from Monte Alpha and Friday seamounts have Sr and Nd isotopic ratios lying on the low143Nd/144Nd side of the mantle array (87Sr/86Sr:0.7034–0.7037;143Nd/144Nd:0.51281–0.51289). The homogeneity of these tracers suggests the involvement of a restricted range of mantle source compositions throughout Juan Fernandez volcanism. In marked contrast is the large range in3He/4He, from 7.8 to 18.0 RA. A bimodal3He/4He distribution on Mas a Tierra is associated with two distinct volcanic lineages;3He/4He ratios of 14.5–18.0 RA (n=15) occur in alkalic and tholeiitic shield basalts, whereas post-shield basanites range from 11.2 to 13.6 RA (n=12). Elemental and isotopic systematics demonstrate a transition from an enriched (Loihi-like) plume source in the shield lavas to a more MORB-like source in the post-shield volcanics. The transition between these sources is much more pronounced in3He/4He than in the other isotopic tracers. The predominantly tholeiitic basalts of Mas Afuera have exceptionally uniform isotopic and elemental characteristics; Sr and Nd ratios are similar to those of Mas a Tierra, but3He/4He ratios are lower and more uniform at 8.3±0.5 RA (n=17). The dramatic distinction between Mas Afuera and Mas a Tierra helium is surprising given the great similarity between the two islands in other geochemical characteristics. Both the Mas Afuera and Mas a Tierra results demonstrate that helium records systematic processes not readily apparent from other isotopic or elemental indicators. Neither magma chamber degassing nor local metasomatic events are likely to be responsible. We suggest that the observed variations may be attributed to mixing of plume and asthenospheric sources in which the plume component is characterized by a heterogeneous distribution of volatiles or has suffered extraction of small degree partial melts prior to mixing. 相似文献
Major- and rare-earth-element (REE) concentrations and UThPb, SmNd, and RbSr isotope systematics are reported for Cenozoic volcanic rocks from northeastern and eastern China. These volcanic rocks, characteristically lacking the calc-alkaline suite of orogenic belts, were emplaced in a rift system which formed in response to the subduction of the western Pacific plate beneath the eastern Asiatic continental margin. The rocks sampled range from basanite and alkali olivine basalt, through olivine tholeiite and quartz tholeiite, to potassic basalts, alkali trachytes, pantellerite, and limburgite. These rock suites represent the volcanic centers of Datong, Hanobar, Kuandian, Changbaishan and Wudalianchi in northeastern China, and Mingxi in the Fujian Province of eastern China.The major-element and REE geochemistry is characteristic of each volcanic suite broadly evolving through cogenetic magmatic processes. Some of the outstanding features of the isotopic correlation arrays are as follows: (1) NdSr shows an anticorrelation within the field of ocean island basalts, extending from the MORB end-member to an enriched, time-averaged high Rb/Sr and Nd/Sr end-member (EM1), (2) SrPb also shows an anticorrelation, similar to that of Hawaiian and walvis Ridge basalts, (3) NdPb shows a positive correlation, and (4) the 207Pb/204Pb vs 206Pb/204Pb plot shows linear arrays parallel to the general trend (NHRL) for MORB on both sides of the geochron, although in the 208Pb/204Pb vs 206Pb/204Pb plot the linear array is significantly displaced above the NHRL in a pattern similar to that of the oceanic island basalts that show the Dupal signatures. In all isotope correlation patterns, the data arrays define two different mantle components—a MORB-like component and an enriched mantle component. The isotopic data presented here clearly demonstrate the existence of Dupal compositions in the sources of the continental volcanic rocks of eastern China. We suggest that the subcontinental mantle beneath eastern China served as the reservoir for the EMI component, and that the MORB component was either introduced by subduction of the Kula-Pacific Ridge beneath the Asiatic plate in the Late Cretaceous, as proposed by Uyeda and Miyashiro, or by upwellings in the subcontinental asthenosphere due to subduction. 相似文献