Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.     

An Example of Island-Arc Petrogenesis: Geochemistry and Petrology of the Southern Luzon Arc, Philippines

Volcanism throughout the Luzon arc is associated with eastwardsubduction of the South China Sea floor along the Manila Trench.The southern section of the arc, the focus of this study, extendsfrom the Lingayen-Dingalan fault to the small islands just southof Luzon. Two segments appear to exist along this section ofthe arc the northern Bataan and southern Mindoro segments whichare separated by the Macolod Corridor. The volcanic rocks have typical arc phenocryst mineralogies:olivine, clinopyroxene, plagioclase, and titanomagnetite inthe most mafic rocks and clinopyroxene, plagioclase, orthopyroxene,titanomagnetite, ? amphibole in the more felsic samples. Complexzoning, sieve textures, and decoupling of incompatible traceelements suggest that processes such as assimilation have takenplace. The rocks from the study area range from basalts to rhyolitesand show typical calc-alkaline features. The rocks of the MacolodCorridor and Mindoro segment are particularly enriched in largeion lithophile elements (LILE), light rare earth elements (LREE),and radiogenic Sr compared with the Bataan segment. The datafall within the mantle array on Sr-Nd isotopic diagrams andgrade toward higher Sr and lower Nd isotopic values from northto south. A likely source for the volcanics of this study is either amid-ocean ridge basalt (MORB)-type mantle that undergoes higherdegrees of partial melting than regions involved in MORB generationor a previously depleted source. We suggest that the high fieldstrength element (HFSE) anomalies have been derived throughdifferential element partitioning during fluid transport fromthe subducted lithosphere to the mantle wedge. Continental crustal material seems to play a significant roleparticularly in the Macolod Corridor and the Mindoro segment,based on the high LILE, La/Sm ratios, radiogenic Sr isotopes,and ¹⁸O values. The Macolod Corridor and the Mindoro segmenthave undergone source contamination by crustal material fromthe North Palawan-Mindoro crustal block either during the collisionof this block with the Manila Trench or by subduction of sedimentsrich in this crustal material. A similar component has alsobeen detected in the Bataan segment but in minor amounts. Thetrace element and isotopic differences between the northernand southern sections of the arc are interpreted in terms ofvariable composition (i. e., variable amounts of a crustal componentintroduced from the Palawan-Mindoro crustal terrain) of themetasomatic fluids released into the source.     

Applications of particle-tracking techniques to bank infiltration: a case study from El Paso,Texas, USA

This paper presents results of a small scale study that utilized particle-tracking techniques to evaluate transport of river water through an alluvial aquifer in a bank infiltration testing site in El Paso, Texas, USA. The particle-tracking survey was used to better define filtration parameters. Several simulations were generated to allow visualization of the effects of well placement and pumping rate on flow paths, travel time, the size of the pumping influence zone, and proportion of river-derived water and groundwater mixing in the pumping well. Simulations indicate that migration of river water into the aquifer is generally slow. Most water does not arrive at the well by the end of an 18-day pumping period at 0.54 m³/min pumping rate for a well located 18 m from the river. Forty-four percent of the water pumped from the well was river water. The models provided important information needed to design appropriate sampling schedules for bank filtration practices and ensured meeting adequate soil-retention times. The pumping rate has more effect on river water travel time than the location of the pumping well from the river. The examples presented in this paper indicate that operating the pumping well at a doubled distance from the river increased the time required for the water to travel to the well, but did not greatly change the capture zone.     

Modeling of water–rock interactions in an aquitard of sandy clay in the coastal area near Beihai,China

Unconsolidated sand, gravel and clay deposits near Beihai and in the Leizhou Peninsula in southern China form an unconfined aquifer, aquitard and a confined aquifer. Water and soil samples were collected from the two aquifers in the coastal Beihai area for the determination of chemical compositions, minerals and soluble ions. Hydrogeochemical modeling of three flow paths through the aquitard are carried out using PHREEQC to determine water–rock interactions along the flow paths. The results indicate that the dissolution of anorthite, fluorite, halite, rhodochrosite and CO₂, and precipitation of potash feldspar and kaolinite may be occurring when groundwater leaks through the aquitard from the unconfined aquifer to the confined aquifer. Cation exchanges between Na and Ca can also happen along the flow paths.     

An operational multiscale system for hazards prediction, mapping, and response

By definition, a crisis is a situation that requires assistance to be managed. Hence, response to a crisis involves the merging of local and non-local emergency response personnel. In this situation, it is critical that each participant: (1) know the roles and responsibilities of each of the other participants; (2) know the capabilities of each of the participants; and (3) have a common basis for action. For many types of natural disasters, this entails having a common operational picture of the unfolding events, including detailed information on the weather, both current and forecasted, that may impact on either the emergency itself or on response activities. The Consequences Assessment Tool Set (CATS) is a comprehensive package of hazard prediction models and casualty and damage assessment tools that provides a linkage between a modeled or observed effect and the attendant consequences for populations, infrastructure, and resources, and, hence, provides the common operational picture for emergency response. The Operational Multiscale Environment model with Grid Adaptivity (OMEGA) is an atmospheric simulation system that links the latest methods in computational fluid dynamics and high-resolution gridding technologies with numerical weather prediction to provide specific weather analysis and forecast capability that can be merged into the geographic information system framework of CATS. This paper documents the problem of emergency response as an end-to-end system and presents the integrated CATS–OMEGA system as a prototype of such a system that has been used successfully in a number of different situations.     

Diel Patterns in Chlorophyll <Emphasis Type="Italic">a</Emphasis> Specific Absorption Coefficient and Absorption Efficiency Factor of Picoplankton

Diel patterns in the chlorophyll a specific absorption coefficient of surface picoplankton, a*_pico (γ) (m²·[mg chlorophyll a]⁻¹), were studied at 7 stations under daily cycle of in situ light condition in the western subarctic Pacific and Japan Sea. All the data were normalized by dividing the anomaly with daily averaged a*_pico (γ). Opposite diel patterns were observed for the normalized a*_pico (443) and a*_pico (675) with maximum toward dawn or dusk and minimum toward midday at 4 stations under low-irradiance (LI) conditions and vice versa at 3 stations under high-irradiance (HI) conditions. The absorption efficiency factors at red absorption peak, Q _a (675), were determined by reconstruction with intracellular chlorophyll a concentration and cell diameter. The normalized Q _a (675) also showed diel pattern with maximum toward midday and minimum toward dawn or dusk under LI. The diel pattern in a*_pico (675) and Q _a (675) were primarily caused by changes in intracellular chlorophyll a concentration due to photoadaptation under LI. The diel pattern in a*_pico (443) was influenced by pigmentation, as recognized by blue to red ratio [a*_pico (443)/a*_pico (675)] under HI. This study proposed that the opposite diel pattern in a*_pico (γ) might occur for a wide range of algal species. The results presented here have important consequences for the interpretation of diel variations in optical properties observed in the open ocean.     

CO<Subscript>2</Subscript> Flux Measurements over the Sea Surface by Eddy Correlation and Aerodynamic Techniques

The measurements of the vertical transport of CO₂ were carried out over the Sea of Japan using the specially designed pier of Kyoto University on September 20 to 22, 2000. CO₂ fluxes were measured by the eddy correlation and aerodynamic techniques. Both techniques showed comparable CO₂ fluxes during sea breeze conditions: −0.001 to −0.08 mg m⁻²s⁻¹ with the mean of −0.05 mg m⁻²s⁻¹. This means that the measuring site satisfies the fetch requirement for meteorological observations under sea breeze conditions. Moreover, the eddy diffusivity coefficient used in the aerodynamic technique is found to be consistent with the coefficient used in the eddy correlation technique. The present result leads us to conclude that the aerodynamic technique may be applicable to underway CO₂ flux measurements over the ocean and may be used in place of the bulk technique. The important point is the need to maintain a measuring accuracy of CO₂ concentration difference of the order of 0.1 ppmv on the research vessels or the buoys.