Some exact solutions for the flow of fluid through tubes with uniformly porous walls

Summary This paper considers an incompressible fluid flowing through a straight, circular tube whose walls are uniformly porous. The flow is steady and one dimensional. The loss of fluid through the wall is proportional to the mean static pressure in the tube. Several formulations of the wall shear stress are considered; these formulations were motivated by the results from Hamel's radial flow problem, boundary layer flows/and boundary layer suction profiles. For each of these formulations exact solutions for the mean axial velocity and the mean static pressure of the fluid are obtained. Sample results are plotted on graphs. For the constant wall shear stress problem, the theoretical solutions compare favorably with some experimental results.Notations A, B, D, E constant parameters - a, b constant parameters - Ai(z), Bi(z) Airy functions - Ai, Bi derivatives of Airy functions - k constant of proportionality betweenV andp - L length of pores - p,p mean static pressure - p ₀ static pressure outside the tube - p ₀ value ofp atx=0 - Q constant exponent - R inside radius of the tube - T wall shear stress - T ₀ shear parameter - t wall thickness - U free stream velocity - ,u mean axial velocity - u ₀ value ofu atx=0 - V,V mean seepage velocity through the wall - v ₀ mean seepage velocity - x,x axial distance along the tube - z transformed axial distance - z ₀ value ofz atx=0 - mean outflow angle through the wall - cos - density of the fluid - wall shear stress - dynamic viscosity of the fluid - over-bar dimensional terms - no bar nondimensional terms The National Center for Atmospheric Research is sponsored by the National Science Foundation     

Equilibrium temperatures of interstellar iron grains

Because of the relatively low number densities found in typical interstellar clouds, molecules observed there must be produced by a combination of both two-body gas-phase reactions and surface reactions. The latter type includes various catalytic reactions, such as the formation of H₂ on transition metal grains. These reactions are very temperature dependent, the grain temperature appearing in the exponential of the rate equations. Because of the small heat capacities of the grains due to their small sizes, they may be subject to considerable fluctuations in temperature. This problem is examined for iron grains and found to be minimal for sizes greater than 100 Å. Steady-state equilibrium temperatures are then calculated for a size distribution of iron particles ranging from 10³ to 10⁹ atoms per grain by a refined method of an earlier work by one of us (RGT). The results are that iron grain temperatures are significantly greater than those of dielectric grains of comparable size in the same radiation field.     

Numerical Simulation of Strongly Stratified Flow Over a Three-Dimensional Hill

A numerical study of stably stratified flow over a three-dimensional hill is presented. Large-eddy simulation is used here to examine in detail the laboratory experimental flows described in the landmark work of Hunt and Snyder about stratified flow over a hill. The flow is linearly stratified and U/Nh is varied from 0.2 to 1.0. Here N and U are the buoyancy frequency and freestream velocity respectively, and h is the height of the hill. The Reynolds number based on the hill height is varied from 365 to 2968. The characteristic flow patterns at various values of U/Nh have been obtained and they are in good agreement with earlier theoretical and experimental results. It is shown that the flow field cannot be predicted by Drazin's theory when recirculation exists at the leeside of the hill even at UNh 1. The wake structure agrees well with a two-dimensional wake assumption when U/Nh 1 but lee waves start to influence the wake structure as U/Nh increases. The dividing-streamline heights obtained in the simulation are in accordance with experimental results and Sheppard's formula. The energy loss along the dividing streamline due to friction/turbulence approximately offsets the energy gained from pressure field. When lee waves are present, linear theory always underestimates the amplitude and overestimates the wavelength of three-dimensional lee waves. The simulated variations of drag coefficients with the parameterK (=ND/ U) are qualitatively consistent with experimental data and linear theory. Here D is the depth of the tank.     

Contaminant concentrations in sport fish from San Francisco Bay, 1997

In 1997, seven sport fish species were sampled from seven popular fishing areas in San Francisco Bay. Mercury exceeded a human health screening value in 44 of 84 (52%) samples. All collected samples of leopard shark and striped bass exceeded the mercury screening value of 0.23 microg/g wet weight. PCBs exceeded the screening value in 51 of 72 (71%) samples. DDT, chlordane, and dieldrin, had lower numbers of samples above screening values: 16 of 72 (22%) for DDT, 11 of 72 (15%) for chlordanes, and 27 of 72 (37%) for dieldrin. Concentrations of PCBs and other trace organics were highest in white croaker and shiner surfperch, the two species with the highest fat content in their muscle tissue. Fish from one location, Oakland Harbor, had significantly elevated wet weight concentrations of mercury, PCBs, DDTs, and chlordanes compared to other locations. Removal of skin from white croaker fillets reduced lipid concentrations by 27-49% and concentrations of trace organics by 33-40%.     

Spatial and temporal variability of mesozooplankton and tintinnid ciliates in a seasonally hypersaline estuary

The zooplankton community of Mission Bay, San Diego, California, was monitored over two years, to study spatial and temporal patterns and the response of zooplankton species composition to environmental variation. Data were collected every two weeks from six stations and included hydrographic parameters, dissolved nutrient concentrations, and phytoplankton and zooplankton species composition. Hydrography varied seasonally, along a spatial gradient from the mouth to the back of the bay, and between the two years around the influence of rainfall. Spatially, Mission Bay could be divided into three regions during this study based on hydrography and zooplankton species composition. Zooplankton species composition followed a predictable seasonal progression, with different groups of species being characteristic to particular times of the year. Variability in zooplankton species composition was also evident between years, as certain species were more common in one or the other year of the study. Spatial patterns were more consistent than temporal ones, and related to distance from the mouth of the bay during much of the year and distance from freshwater inlets during the relatively short rainy season. Multivariate analysis revealed that variation in zooplankton species composition was best related to measured abiotic factors (temperature, salinity, rainfall, and tidal velocity).     

Pleistocene tectonics inferred from fluvial terraces of the northern Upper Rhine Graben, Germany

This study of fluvial terraces of the River Rhine and tributaries aims to search for indications of Pleistocene tectonic activity. The study area includes the northern Upper Rhine Graben (URG), the Mainz Basin and the adjacent Rhenish Massif with the Middle Rhine Valley. High rates of Quaternary surface processes, large amount of human modifications, relatively slow tectonic deformation and presently low intra-plate seismic activity characterize this area. Therefore, the records of relatively slow tectonic deformation are less well preserved and thus difficult to detect. This study uses the relative position of fluvial terraces to determine the more local effects of fault movements on the terraces and to evaluate their displacement rates and patterns. The research is based on a review of previous terrace studies and new terrace mapping from the eastern Mainz Basin and the bordering URG using topographic map interpretations and field observations. This newly mapped sequence of terrace surfaces can be correlated to other terraces in the vicinity on the basis of relative height levels. Terrace correlation between the western Mainz Basin and Middle Rhine Valley relies on a single chronostratigraphic unit (Mosbach sands) and additional relative height correlations. This is the first study to present a continuous correlation of terraces from the western margin of the URG to the Rhenish Massif and enables the study of the transition from the subsiding graben to the uplifted Rhenish Massif. By means of a longitudinal profile, which ranges from the URG to the Rhenish Massif, the influence of individual fault movements on the terrace levels and the large-scale regional uplift is demonstrated. It is evident from the profile that the uplift of Early to Middle Pleistocene terraces increases northwards, towards the Rhenish Massif. The uplift was diachronic, with a significant pulse occurring first in the northern URG (Lower Pleistocene) and later in the Rhenish Massif (Middle Pleistocene). The largest vertical displacements are recorded for the boundary fault separating the Mainz Basin and the Rhenish Massif (Hunsrück–Taunus Boundary Fault) and for faults bounding the northeastern Mainz Basin. The motions and displacement rates calculated for individual faults indicate deformation rates in the order of 0.01–0.08 mm/year. At this stage, the calculation of displacement rates depends mostly on a single dated stratigraphic unit. Additional dating of terrace deposits is urgently needed to better constrain the temporal development of the terrace sequence and the impact of tectonic movements.     

INTEGRATION OF THE MODELS OF ANNAGNPS AND REMM TO ASSESS RIPARIAN BUFFER SYSTEM FOR SEDIMENT REDUCTION

The United States Department of Agriculture (USDA) Annualized Agricultural Non-Point Source Pollution model (AnnAGNPS) is used to help evaluate a watershed response to agricultural management practices to control water quality. However, AnnAGNPS version 3.5 does not contain features to estimate the effect of a riparian buffer (RB) system on water quality. The Riparian Ecosystem Management Model (REMM) is used to simulate the impact of riparian buffer systems on water quality. However, frequently the lack of measured upland loadings that are required by REMM simulation limits the application of REMM. To address this data gap, a study was conducted to integrate AnnAGNPS with REMM for RB system simulation. AnnAGNPS was used to simulate water and sediment loadings from an upland field into a three-zone RB system at the Gibbs Farm located in the Georgia coastal plain. These AnnAGNPS outputs were used as the inputs to REMM. REMM was used to simulate water and sediment movement along the riparian buffers. The AnnAGNPS simulated amount of annual runoff at the edge of the field was close to observed amounts (Nash-Sutcliffe efficiency of 0.92). It is believed that a substantial portion of sand was removed from the runoff one meter into the grass buffer where the samplers were located; therefore, sand was excluded from the AnnAGNPS simulation for comparison with observed sediment. Excluding sand, the AnnAGNPS predicted amount of annual sediment matches the observed amount fairly well (Nash-Sutcliffe efficiency of 0.46). In addition, based on evaluating the percent reduction of sediment at each zonal interface, the AnnAGNPS/REMM model well simulated the function of the RB system to reduce sediment.     

Context and climate change: an integrated assessment for Barrow, Alaska

An intensive approach to Barrow, Alaska’s adaptations to climate change and variability during recent decades suggests reconsideration of the interconnected roles of science, policy, and decision-making structures. First, profound uncertainties are inherent in unique interactions among the many natural and human factors affecting Barrow’s vulnerability. Science cannot significantly reduce these uncertainties through extensive approaches, but intensive approaches can reconstruct and update local trends, clarify the underlying dynamics, and harvest experience for policy purposes. Second, sound policies to reduce Barrow’s vulnerability to coastal erosion and flooding must incorporate these profound uncertainties and the multiple values of the community. Minimizing vulnerability to climate change is only one of the community’s interests, and must compete with other interests for limited time, attention, funds and other resources. Third, the community itself is in the best position to understand its own context, to decide on sound policies, and to take responsibility for those decisions. In short, local context matters in science, policy, and decision-making structures for adaptation to climate change and variability. Overall, cognitive constraints may be the most important human dimension of climate change. Factoring the global problem into more tractable local problems would make the most of our cognitive capacity.     

U-Series Chronology of Lacustrine Deposits in Death Valley, California

Uranium-series dating on a 186-m core (DV93-1) drilled from Badwater Basin in Death Valley, California, and on calcareous tufas from nearby strandlines shows that Lake Manly, the lake that periodically flooded Death Valley during the late Pleistocene, experienced large fluctuations in depth and chemistry over the last 200,000 yr. Death Valley has been occupied by a long-standing deep lake, perennial shallow saline lakes, and a desiccated salt pan similar to the modern valley floor. The average sedimentation rate of about 1 mm/yr for core DV93-1 was punctuated by episodes of more-rapid accumulation of halite. Arid conditions similar to the modern conditions prevailed during the entire Holocene and between 120,000 and 60,000 yr B.P. From 35,000 yr B.P. to the beginning of the Holocene, a perennial saline lake existed, over 70 m at its deepest. A much deeper and longer lasting perennial Lake Manly existed from about 185,000 to 128,000 yr B.P., with water depths reaching about 175 m, if not 330 m. This lake had two significant “dry” excursions of 10²–10³yr duration about 166,000 and 146,000 yr B.P., and it began to shrink to the point of halite precipitation between 128,000 and 120,000 yr B.P. The two perennial lake periods correspond to marine oxygen isotopic stages (OIS) 2 and 6. Based on the shoreline tufa ages, we do not rule out the possible existence 200,000 yr ago of yet a third perennial lake comparable in size to the OIS 6 lake. The²³⁴U/²³⁸U data suggest that U in tufa owes its origin mainly to Ca-rich springs fed by groundwater that emanated along lake shorelines in southern Death Valley, and that an increase of this spring-water input relative to the river-water input apparently occurred during OIS 6.