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The shear-free turbulent boundary layer is calculated by the large-eddy simulation technique. The filtered Navier-Stokes equations are used; the method of integration employs Fourier expansions in the homogeneous directions and finite differences in the cross-stream direction. Results indicate that the simulation is capable of predicting the primary Reynolds-number effects.
Two stream methods provide rapid approximate calculations of radiative transfer in scattering and absorbing media. Although they provide information on fluxes only, and not on intensities, their speed makes them attractive to more precise methods. The methods provide a comprehensive, unified review for a homogeneous layer, and solve the equations for reflectance and transmittance for a homogeneous layer over a non reflecting surface. Any of the basic kernels for a single layer can be extended to a vertically inhomogeneous medium over a surface whose reflectance properties vary with illumination angle, as long as the medium can be subdivided into homogeneous layers.
An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.
We examined the distribution of surface slopes of a variety of terrestrial surfaces by field measurement, representing surfaces formed by a wide range of processes, and compared the results to planetary radar data. Slope distributions of the measured surfaces differed considerably from the distributions assumed by accepted models of radar scattering. We also used Hagfors' model of radar scattering to predict the return that would be expected from surfaces where two discrete surface types were present within the radar field of view and found that the shapes of the resulting slope distributions differed from those predicted by the Hagfors model for homogeneous surfaces. Together, these results suggest that current methods of determining surface roughness from radar may significantly underestimate the roughness of planetary surfaces and that the derived rms slope can best be used as a qualitative guide to the physical interpretation of actual surface properties.
Spatiotemporal variability in the carbon isotope composition of sedimentary organic matter (OM) preserves information about the evolution of the biosphere and of the exogenic carbon cycle as a whole. Primary compositions, and imprints of the post-depositional processes that obscure them, exist at the scale of individual sedimentary grains (mm to micron). Secondary ion mass spectrometry (SIMS) (1) enables analysis at these scales and in petrographic context, (2) permits morphological and compositional characterization of the analyte and associated minerals prior to isotopic analysis, and (3) reveals patterns of variability homogenized by bulk techniques. Here we present new methods for in situ organic carbon isotope analysis with sub-permil precision and spatial resolution to 1 micron using SIMS, as well as new data acquired from a suite of Archean rocks. Three analytical protocols were developed for the CAMECA ims1280 at WiscSIMS to analyze domains of varying size and carbon concentration. Average reproducibility (at 2SD) using a 6 micron spot size with two Faraday cup detectors was 0.4 %, and 0.8 % for analyses using 1 micron and 3 micron spot sizes with a Faraday cup (for C-12) and an electron multiplier (for C-13). Eight coals, two ambers, a shungite, and a graphite were evaluated for micron-scale isotopic heterogeneity, and LCNN anthracite (delta C-13 = -23.56 +/- 0.1 %, 2SD) was chosen as the working standard. Correlation between instrumental bias and H/C was observed and calibrated for each analytical session using organic materials with H/C between 0.1 and 1.5 (atomic), allowing a correction based upon a C-13H/C-13 measurement included in every analysis. Matrix effects of variable C/SiO2 were evaluated by measuring mm to sub-micron graphite domains in quartzite from Bogala mine, Sri Lanka. Apparent instrumental bias and C-12 count rate are correlated in this case, but this may be related to a crystal orientation effect in graphite. Analyses of amorphous Archean OM suggest that instrumental bias is consistent for 12C count rates as low as 10% relative to anthracite. Samples from the ABDP-9 (n=3; Mount McRae Shale, approximately 2.5 Ga), RHDH2a (n=2; Carrawine Dolomite and Jeerinah Fm, approximately 2.6 Ga), WRL1 (n=3; Wittenoom Fm, Marra Mamba Iron Formation, and Jeerinah Fm, approximately 2.6 Ga), and SV1 (n=1; Tumbiana Fm, approximately 2.7 Ga) drill cores, each previously analyzed for bulk organic carbon isotope composition, yielded 100 new, in situ data from Neoarchean sedimentary OM. In these samples, delta C-13 varies between -53.1 and -28.3 % and offsets between in situ and bulk compositions range from -8.3 to 18.8%. In some cases, isotopic composition and mode of occurrence (e.g. morphology and mineral associations) are statistically correlated, enabling the identification of distinct reservoirs of OM. Our results support previous evidence for gradients of oxidation with depth in Neoarchean environments driven by photosynthesis and methane metabolism. The relevance of these findings to questions of bio- and syngenicity as well as the alteration history of previously reported Archean OM will be discussed.
High-resolution soft X-ray spectroscopic observations of single hot white dwarfs are scarce. With the Chandra Low-Energy Transmission Grating, we have observed two white dwarfs, one is of spectral type DA (LB1919) and the other is a non-DA of spectral type PG1159 (PG1520+525). The spectra of both stars are analyzed, together with an archival Chandra spectrum of another DA white dwarf (GD246). Aims. The soft X-ray spectra of the two DA white dwarfs are investigated in order to study the effect of gravitational settling and radiative levitation of metals in their photospheres. LB1919 is of interest because it has a significantly lower metallicity than DAs with otherwise similar atmospheric parameters. GD246 is the only white dwarf known that shows identifiable individual iron lines in the soft X-ray range. For the PG1159 star, a precise effective temperature determination is performed in order to confine the position of the blue edge of the GW Vir instability region in the HRD. Methods. The Chandra spectra are analyzed with chemically homogeneous as well as stratified NLTE model atmospheres that assume equilibrium between gravitational settling and radiative acceleration of chemical elements. Archival EUV and UV spectra obtained with EUVE, FUSE, and HST are utilized to support the analysis. Results. No metals could be identified in LB1919. All observations are compatible with a pure hydrogen atmosphere. This is in stark contrast to the vast majority of hot DA white dwarfs that exhibit light and heavy metals and to the stratified models that predict significant metal abundances in the atmosphere. For GD246 we find that neither stratified nor homogeneous models can fit the Chandra spectrum. The Chandra spectrum of PG1520+525 constrains the effective temperature to T(sub eff) = 150 000 +/- 10 000 K. Therefore, this nonpulsating star together with the pulsating prototype of the GWVir class (PG1159-035) defines the location of the blue edge of the GWVir instability region. The result is in accordance with predictions from nonadiabatic stellar pulsation models. Such models are therefore reliable tools to investigate the interior structure of GW Vir variables. Conclusions. Our soft X-ray study reveals that the understanding of metal abundances in hot DA white dwarf atmospheres is still incomplete. On the other hand, model atmospheres of hydrogen-deficient PG1159-type stars are reliable and reproduce well the observed spectra from soft X-ray to optical wavelengths.
A new numerical algorithm is developed and applied to the direct simulation of compressible, homogeneous turbulent flows at low Mach numbers. A split method in time first solves a subset of the equations explicitly, followed by an implicit treatment of the pressure terms. The definition of an average sound speed over the entire field allows the implicit equations to be solved analytically, while relaxing the severe time limit imposed by the large sound speeds. Results from direct simulations on 96(3) grids provide a data base against which a new subgrid-scale model for compressible homogeneous turbulence is tested. This model reduces to the linear combination model in the absence of compressibility.
A numerical method is presented for calculating the incompressible boundary-induced interference in wind tunnels of rectangular cross section with slotted or perforated walls. The method includes a wall representation which is capable of satisfying a generalized homogeneous boundary condition including the effects of viscosity within the slots. The effects of viscosity in the slots are found to be very significant. The method allows for a variation in the boundary conditions along the tunnel walls. The model can be any configuration and can be located anywhere in the test section. The interference can be computed at any point in the test section.
A version of the two step Lax-Wendroff difference method with second order accuracy is used to seek solutions of the unsteady magnetohydrodynamic (MHD) equations for the study of an explosion in a non-homogeneous medium with and without magnetic fields. The explosion is initiated by introducing a finite amount of energy in a small volume of gas which leads to an instantaneous increase of gas temperature. Two types of magnetic field configurations (i.e. open and closed) are considered to illustrate the dependence and differences of magnetic and a non-magnetic flow motion. Numerical results show the strong dependence of induced MHD flow field on the magnetic field configuration and strength. The development and decay of the fast and slow MHD shock waves, as well as the ordinary gasdynamic shock waves, are also represented well by the present computer simulations. In conclusion, we have demonstrated that the numerical scheme we have used is a reliable one for studying 2-dimensional MHD problems in non-homogeneous medium.
We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.
We critically evaluate current methods of analysis in infrared (IR) astronomy and investigate the conditions under which these semianalytic methods are reliable. Specifically we examine the usual assumptions of homogeneities in dust density and temperature, and neglect of opacity effects when applied to internally heated, unresolved IR sources. To accomplish this, a series of radiation transport models for these sources have been constructed. The model results are treated as observed quantities and analyzed to derive the source parameters, using simple semianalytic methods. The discrepancies between the derived and actual model parameters can then be attributed to the limitations of the analysis methods and provide a measure of their reliability. Applying this approach to centrally heated, unresolved IR sources, we have studied in detail the following diagnostic problems: (1) determination of dust mass from monochromatic and integrated luminosities; (2) estimation of dust temperature distribution from color temperatures derived from the flux spectrum; and (3) determination of the empirical grain emissivity law (opacity function) for both continuum and spectral features.
Use of a simple method based on energy balance to rederive the well-known threshold condition for the purely growing parametric instability in a homogeneous medium and to estimate the effects of inhomogeneity in a semiquantitative manner. A method different from that of Perkins and Flick (1971) is then used to calculate the threshold in a more quantitative manner for the instance where the effects of inhomogeneity dominate over those of collisions. The result agrees with that of Perkins and Flick for k sub parallel l much greater than 1 in their terminology. For k sub parallel much less than 1, neither theory is directly applicable and the threshold is obtained by numerical methods. The present method of calculation has the advantages that its range of validity is easily checked, that it provides good physical insight, and that it is easily applicable to electromagnetic instabilities.
Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.
We present a method for the analysis of spectral line shapes arising in homogeneous, moving gas clouds in which velocity and molecular line excitation have power-law dependences on radial distance from the center. Analytical expressions are obtained for radial flows, for both optically thick and optically thin lines. The additional case of an optically thick line from a differentially rotating cloud is considered qualitatively. The method is applied to the interpretation of the C(12)O line observed in the direction of the Kleinmann-Low infrared nebula in Orion. While gravitational collapse and accelerated outflows would produce lines qualitatively similar to the observed profile, it does not appear to be possible to fit either model to the observations in detail.
Dispersion of guided waves in a cross-ply laminated plate has been studied here using a stiffness method and an exact method. It is shown that the number of laminae strongly influences the dispersion behavior. Further, it is found that when the number of laminae is sufficiently large, then the dispersion behavior can be predicted by treating the plate as homogeneous with six stiffness constants obtained by using an effective modulus method.
The effect of switching between nonstiff and stiff methods on the efficiency of algorithms for integrating chemical kinetic rate equations was examined. Different integration methods were tested by application of the packaged code LSODE to four practical combustion kinetics problems. The problems describe adiabatic, and homogeneous gas phase combustion reactions. It is shown that selective use of nonstiff and stiff methods in different regimes of a typical batch combustion problem is faster than the use of either method for the entire problem. The implications which result in the development of fast integration techniques for combustion kinetic rate equations are discussed.
By using Fourier transforms for evaluating spatial derivatives, the accuracy of the large-eddy simulation of homogeneous isotropic turbulence is improved. Especially, the treatment of certain terms that arise in filtering the equations is considerably improved in both speed and accuracy. Use of vorticity as the principal variable is shown to be a viable and potentially useful alternative to the primitive variables. A method of deriving conservation properties of numerical schemes is given which is much simpler than previous methods and is widely applicable. The methods are applied to the computation of homogeneous isotropic turbulence, and it is found that the subgrid scale model is improved by using finite differences in place of 'exact' derivatives.
The effect of switching between nonstiff and stiff methods on the efficiency of algorithms for integrating chemical kinetic rate equations is presented. Different integration methods are tested by application of the packaged code LSODE to four practical combustion kinetics problems. The problems describe adiabatic, homogeneous gas-phase combustion reactions. It is shown that selective use of nonstiff and stiff methods in different regimes of a typical batch combustion problem is faster than the use of either method for the entire problem. The implications of this result to the development of fast integration techniques for combustion kinetic rate equations are discussed.