Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

Geostatistical features of streambed vertical hydraulic conductivities in Frenchman Creek Watershed in Western Nebraska

This study evaluated the spatial variability of streambed vertical hydraulic conductivity (K_v) in different stream morphologies in the Frenchman Creek Watershed, Western Nebraska, using different variogram models. Streambed K_v values were determined in situ using permeameter tests at 10 sites in Frenchman, Stinking Water and Spring Creeks during the dry season at baseflow conditions. Measurements were taken both in straight and meandering stream channels during a 5 day period at similar flow conditions. Each test site comprised of at least three transects and each transect comprised of at least three K_v measurements. Linear, Gaussian, exponential and spherical variogram models were used with Kriging gridding method for the 10 sites. As a goodness-of-fit statistic for the variogram models, cross-validation results showed differences in the median absolute deviation and the standard deviation of the cross-validation residuals. Results show that using the geometric means of the 10 sites for gridding performs better than using either all the K_v values from the 93 permeameter tests or 10 K_v values from the middle transects and centre permeameters. Incorporating both the spatial variability and the uncertainty involved in the measurement at a reach segment can yield more accurate grid results that can be useful in calibrating K_v at watershed or sub-watershed scales in distributed hydrological models.     

Spectroscopic studies of three novae

We present our spectroscopic observations of the novae V1425, V1493, and V1494 Aql carried out with the 125-cm telescope at the Crimean Station of the Sternberg Astronomical Institute in the wavelength range 4000–11000 Å. We measured the emission-line intensities, determined the nova shell expansion velocities from the line profile FWHMs and components, and estimated the interstellar reddening from the first members of the Balmer series. The chemical composition of the nova shells is analyzed. Nitrogen and oxygen were found to be overabundant in V1425 and V1494 Aql; the helium abundance turned out to be normal in the two stars.     

Pulsar magnetic field for an infinitely conductive accretion disk

The magnetic-field distribution outside a flat, infinitely conductive unbounded disk in the field of a point magnetic dipole is determined. A relationship is established between the problem of magnetic-field determination and the problem of the flow of an ideal incompressible fluid around an infinitely thin disk.     

Gamma-Hadron Separation using Čerenkov Photon Density Fluctuations

In the atmospheric Čerenkov technique γ-rays are detected against the abundant background produced by hadronic showers. In order to improve the signal to noise ratio of theexperiment, it is necessary to reject a significant fraction of hadronic showers. Traditional background rejection methods based on image shape parameters have been extensively used for the data from imaging telescopes. However, non-imaging Čerenkov telescopes have to develop very different means of statistically identifying and removing cosmic ray events. Some of the parameters, which could be potentially important for non-imaging arrays, are the temporal and spectral differences, the lateral distributions and density fluctuations of Čerenkov photons generated by γ-ray and hadron primaries. Here we study the differences in fluctuations of Čerenkov photon density in the light pool at the observation level from showers initiated by photons and those initiated by protons or heavier nuclei. The database of simulated events for the PACT array has been used to evaluate the efficiency of the new technique. Various types of density fluctuations like the short range and medium range fluctuations as well as flatness parameter are studied. The estimated quality factors reflect the efficiencies with which the hadrons can be rejected from the data. Since some of these parameters are independent, the cuts may be applied in tandem and we demonstrate that the proton rejection efficiency of ∼90% can be achieved. Use of density fluctuations is particularly suited for wavefront sampling observations and it seems to be a good technique to improve the signal to noise ratio. This revised version was published online in July 2006 with corrections to the Cover Date.