Non-isotropic Component Research Articles

The Spatial Structure of Passively Simulated Atmospheric Boundary Layer Turbulence

Three types of turbulence fields were investigated using a research method combining wind tunnel tests and theoretical analysis to further explore the spatial structure of atmospheric boundary layer turbulence, which was passively simulated by a wind tunnel. The fundamental theory of turbulence is introduced, and some traditional theoretical coherence models based on isotropic turbulence theory are derived. The difference between the theoretical results and the passive simulation of atmospheric boundary layer turbulence was compared and discussed. The analysis results show that the passively simulated atmospheric turbulence basically conformed to the homogeneous isotropic turbulence assumption on the horizontal plane, but the interference of the nonisotropic turbulence components cannot be ignored either. Finally, some improvements were made to the traditional coherence function model based on the experimental results to apply the passively simulated atmospheric boundary layer turbulence.

The 4 January 2006 (Mw 6.6), San Pedro Martir Earthquake: Example of an Earthquake for Calibrating Excitation and Attenuation Studies

AbstractAn earthquake of magnitude 6.6 occurred on 4 January 2006, at 28.081° N and 112.381° W along a transform fault that joins the San Pedro Martir and the Guaymas basins in the Gulf of California extensional province. We located 17 foreshocks and 38 aftershocks. The foreshocks occurred on a fault perpendicular to the transform fault, where the main event occurred. The aftershocks were located along a fault length of approximately 18 km with a northwest–southeast trend. The average Brune static stress drop of the San Pedro Martir event was 8 MPa. From a time‐domain moment tensor inversion, we obtained the fault geometry given by strike of 129°±1°, dip of 86°±4°, and rake of 168°±12°, which was constrained to have a nonisotropic component and a source depth of 6±2 km. We used the inversion code from Yagi et al. (1999) to invert near field and teleseismic P waves to obtain the spatial slip distribution over the fault. The event had a single source and a moment rate function (MRF) displaying a triangular shape with a duration of 12 s. The rupture propagated toward the northwest from the hypocenter over a rupture area of 28×12 km2 with a maximum slip displacement of 2.3 m and a seismic moment of 8.79×1018 N·m. The directivity confirmed that the rupture propagated from the southeast to the northwest. Few aftershocks were located in the rupture area obtained from the inversion. Most aftershocks occurred toward the southeast of the epicenter. All these source analyses were performed to have a well‐calibrated excitation term for future regional modeling of ground‐motion parameters. The magnitudes of the foreshocks preceding this peculiar earthquake were higher than those of the aftershocks. Our results show that earthquakes with magnitudes of five or higher present a simple and self‐scaling law using a constant stress parameter, but for earthquakes with magnitudes lower than five, the high frequencies are depleted, and the earthquake can be replicated by a low‐stress parameter of 0.28 MPa. We also observed that the aftershocks and foreshocks differ in their frequency content. Although the foreshocks follow Brune’s omega‐squared source term, the aftershocks have larger contents of high frequencies.

Microstructural Rearrangements and their Rheological Implications in a Model Thixotropic Elastoviscoplastic Fluid.

We identify the sequence of microstructural changes that characterize the evolution of an attractive particulate gel under flow and discuss their implications on macroscopic rheology. Dissipative particle dynamics is used to monitor shear-driven evolution of a fabric tensor constructed from the ensemble spatial configuration of individual attractive constituents within the gel. By decomposing this tensor into isotropic and nonisotropic components we show that the average coordination number correlates directly with the flow curve of the shear stress versus shear rate, consistent with theoretical predictions for attractive systems. We show that the evolution in nonisotropic local particle rearrangements are primarily responsible for stress overshoots (strain-hardening) at the inception of steady shear flow and also lead, at larger times and longer scales, to microstructural localization phenomena such as shear banding flow-induced structure formation in the vorticity direction.

Acoustic Wave Refraction in Open Turbulent Flames

Noise generated by combustion processes has attracted the aeroacoustics community's interest especially during the last decade. The classical theories [1, 2] state open turbulent flames being acoustic radiators of mainly monopole type. This has been confirmed by various experiments and numerical simulations [3, 4]. A weak non-isotropic component of the acoustic field has also been observed. In several investigations it was suspected the deviations from the isotropic character of the acoustic field to be related to refraction effects due to the varying mean speed of sound. It is the purpose of this investigation to substantiate this hypothesis. Using the acoustic perturbation equations for reacting flows (APE-RF) the acoustic impact of spatially varying mean speed of sound within a turbulent reacting flow field is numerically investigated. The results show this effect to be frequency dependent and the mean flow field, especially the mean speed of sound, to be taken into account to accurately predict combustion generated noise of open turbulent flames.

Remote sensing of Atmospheric Integrated Water Vapor along Slant Paths Using Ground Based GPS

AbstractSensing of integrated water vapor along slant paths using ground‐based GPS receivers is the basis of getting the three dimensions distribution (water vapor tomography) of water vapor around the observation site. The principle of remote sensing of water vapor along slant paths using GPS is described in this paper. Wet gradient and the post‐fit residuals were used to derive the nonisotropic component of water vapor in different azimuth above the GPS receiver, and then slant path water vapor was derived. In order to validate the accuracy of GPS observation, water vapor radiometers (WVR) were used to observe integrated water vapor along slant paths accompanying the GPS receivers. Comparisons between WVR and GPS observations at different sites and periods show that root‐mean‐square error is less than 4mm. Therefore, slant path water vapor amount can be accurately retrieved using this method, which is suitable for near real‐time application in remote sensing and detection of atmosphere. Ground‐base GPS measurement of water vapor has the advantage of all‐weather continued observation. It is a supplement to traditional water vapor observation and provides accurate continued water vapor data for climate research. The application with GPS receiver network will provide good initial condition for numerical weather prediction and finally contribute to the improvement of weather forecasting accuracy.

Comparison of GPS slant wet delay measurements with model simulations during the passage of a squall line

Slant wet delay (SWD) measurements from a ground‐based GPS observation network provide accurate, high‐resolution moisture information for mesoscale analysis. In this study, we compared SWD simulated from a 9‐km MM5 model in a prefrontal squall line event against actual GPS SWD observations by NOAA's GPS network. We found that the model simulation did not capture abrupt moisture changes and small‐scale variations observed in the nonisotropic component of slant wet delays associated with the squall line. This result suggests that SWD measurements can be very useful in improving model moisture analysis.

Limits on the TeV flux of diffuse gamma rays as measured with the HEGRA air shower array

Using data from the HEGRA air shower array, taken in the period from April 1998 to March 2000, upper limits on the ratio I γ/ I CR of the diffuse photon flux I γ to the hadronic cosmic ray flux I CR are determined for the energy region 20–100 TeV. The analysis uses a gamma–hadron discrimination which is based on differences in the development of photon- and hadron-induced air showers after the shower maximum. A method which is sensitive only to the non-isotropic component of the diffuse photon flux yields an upper limit of I γ/ I CR (at 54 TeV) <2.0×10 −3 (at the 90% confidence level) for a sky region near the inner galaxy (20°< galactic longitude <60° and |galactic latitude |<5°). A method which is sensitive to both the isotropic and the non-isotropic component yields global upper limits of I γ/ I CR (at 31 TeV) <1.2×10 −2 and I γ/ I CR (at 53 TeV) <1.4×10 −2 (at the 90% confidence level).

Isotropic and Nonisotropic Components of Earthquakes and Nuclear Explosions on the Lop Nor Test Site, China

— We test the hypothesis that the existence of an observable non-zero isotropic component of seismic moment can be used as a discriminant to distinguish nuclear explosions from shallow earthquakes. We do this by applying the method described herein to a small set of data recorded between 1990 and 1996 following events (seven nuclear explosions, three earthquakes) that occurred on the Lop Nor test site in Western China. We represent each source as a sum of an isotropic component at the surface and a nonisotropic, double-couple component at an estimated depth. The explosions all possess a significant non-zero isotropic component and the estimated depth of the double-couple component of the moment tensor, presumably the result of tectonic release, lies between about 0 and 3 km. For the earthquakes studied, the isotropic component is indistinguishable from zero and the depths of the sources are estimated at 3, 17 and 31 km. The data set we have studied, although still very small, suggests that certain source characteristics (namely, double-couple depth and the ratio of the isotropic to nonisotropic components of seismic moment) may prove useful in discriminating explosions from shallow earthquakes. Further work is needed to determine whether these observations hold for explosions at other test sites, to investigate a much larger set of shallow earthquakes located in regions of interest, and to study the robustness of the estimated source parameters as source magnitude and the number of observing stations decrease.

Validation of line‐of‐sight water vapor measurements with GPS

We present a direct comparison of nonisotropic, integrated water vapor measurements between a ground‐based Global Positioning System (GPS) receiver and a water vapor radiometer (WVR). These line‐of‐sight water vapor observations are made in the straight line path between a ground station and a GPS satellite. GPS double‐difference observations are processed, and the residual line‐of‐sight water vapor delays are extracted from the double‐difference residuals. These water vapor delays contain the nonisotropic component of the integrated water vapor signal. The isotropic component is represented by the zenith precipitable water vapor measurement and can be scaled to a specific elevation angle based on a mapping function. The GPS observations are corrected for station‐dependent errors using site‐specific multipath maps. The resulting measurements are validated using a WVR which pointed in the direction of the observed satellites. The double‐difference technique used to make these water vapor observations does not depend on accurate satellite clock estimates. Therefore it is especially well suited for near‐real‐time application in weather prediction and allows for sensing atmospheric structure that is below the noise level of current satellite and receiver clock errors. This paper describes the analysis technique and provides precision estimates for the GPS‐measured nonisotropic water vapor as a function of elevation angle for use with data assimilation systems.

Regional crustal trends in South Africa from the spectral analysis of topographic and gravity data

The 2-D spectral analysis of gravity and topography data has been used to identify structural trends of recognized geological entities within the tectonic provinces of South Africa. The mean amplitude of the spectra within very thin rings, taken to have the same mean wavenumber, is subtracted from the total spectrum to give the non-isotropic component. This component of the spectrum reflects more of the heterogeneity of the data and is exploited to produce trends. These results are consistent with known structural trends, but also reveal new trends. Some trends, identified on the Kaapvaal craton using gravity data, are at variance with those obtained from the topography. This suggests that in this area crustal mass distribution is not correlated with surface relief. No dominant structural trend was identified in the Witwatersrand basin. it can be concluded from these findings that this technique can be successfully applied to various data sets, which reflect different physical properties and hence assist in geological interpretation, regardless of the scale.

Elastic Wave Transmission Coefficients and Coupling Loss Factors for Structural Junctions Between Curved Panels

This analysis is concerned with the elastic wave transmission properties of a structural junction at which an arbitrary number of curved panels meet. The generator of each panel is taken to run parallel to the junction line, and the panels may be coupled either directly or via a beam. A "wave dynamic stiffness matrix" approach is presented for the calculation of the junction transmission coefficients, and attention is then turned to the associated coupling loss factors (CLFs) which are required by the Statistical Energy Analysis (SEA) approach to high frequency dynamics. The established notion of a "diffuse wave field" is extended to the case of a non-isotropic component such as a curved panel, and this leads to the derivation of a new expression for the CLFs between such components. It is verified that the new result satisfies the SEA reciprocity relation. Numerical results are presented for two example panel junctions.

Reply to comments by A. Douglas, J. B. Young, and N. S. Lyman and a note on the revised moments for Pahute Mesa tectonic release

In two earlier papers (Wallace et al., 1983, 1985), we discussed the evidence for tectonic release from underground nuclear explosions on Pahute Mesa at the Nevada Test Site (NTS) as observed in long-period body waves. It has been shown for some time that the nonisotropic component of the surface waves from most of these events could be explained by an equivalent double-couple source; namely strike-slip motion on north-striking faults.

Tests concerning two non-isotropic principal components

Kshirsagar & Gupta (1965) proposed test criteria for testing the null hypothesis that a p x p covariance matrix, with known smallest latent root of multiplicity p-2. has its two non-isotropic principal components in specified directions. Simula-tion results indicate that the power functions of these test criteria lack some desirable properties. However, another statis-tic discussed by Kshirsagar and Gupta is shown to have a power-function which performs quite well. The situation in which the smallest latent root of multiplicity p-2 is unknown, is also considered.

On asymptotic distribution of the test statistic for the mean of the non-isotropic principal component

In this paper, the authors derived the large sample distribution of the t statistic based upon the observations on the first principal component instead of the original variables. It is shown that the above statistic is distributed asymptotically as Student's t distribution.

Primordial gravitational waves and the blackbody radiation anisotropy

view Abstract Citations (4) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Primordial gravitational waves and the blackbody radiation anisotropy Adams, P. J. ; Hellings, R. W. ; Zimmerman, R. L. Abstract If relict gravitational waves deriving from a chaotic initial singularity contain a nonisotropic component, then this radiation can produce a frame dragging; effect which will induce a dipole anisotropy in the observed temperature distribution of the 3 K electromagnetic radiation background. The measured dipole and quadrupole distributions of the electromagnetic background can thus be used to bound the effective wave parameters of the nonisotropic part of the gravitational background. Using available data, the dimensionless amplitude of this nonisotropic part is found to be less than 0.0005 for wavelengths less than the Hubble radius. The effective energy density of this nonisotropic component of the gravitational radiation background is less than 2 x 10 to the -8th times the critical density. Publication: The Astrophysical Journal Pub Date: May 1984 DOI: 10.1086/184265 Bibcode: 1984ApJ...280L..39A Keywords: Cosmology; Gravitational Waves; Relic Radiation; Anisotropy; Dipoles; Quadrupoles; Astrophysics full text sources ADS |

Transmittance of diffuse solar radiation through a series of parallel regions

A mathematical formulation is presented for the transmittance of the isotropic and non-isotropic components of diffuse solar radiation through a series of parallel partially transparent regions. The isotropic fraction is determined using a piecewise linear correlation in terms of the clearness index. The non-isotropic fraction is expressed as a shape factor. Results for transmittance through glass plates for several orientations are graphed. (SPH)

The goodness-of-fit of a single (non-isotropic) hypothetical principal component

The goodness-of-fit of a single hypothetical discriminant function in the problem of discrimination between several groups has been considered by Bartlett (1951 a). Virtually, this is the same as testing the adequacy of a single canonical variable to bring out completely the relationship between two vector variables. A single hypothetical canonical variable will be adequate in this 'canonical' or 'external' analysis, if (i) there is only one non-zero canonical correlation, and (ii) the direction of the hypothetical canonical variable coincides with that of the true canonical variable corresponding to the non-zero canonical correlation. Bartlett (1951 a) andWilliams (1952, 1955) have considered these two aspects of' collinearity' and 'direction' in detail, and have derived certain exact tests for them. This situation in 'external' analysis has a parallel in 'internal' or 'principal components' analysis. If the population variance-covariance matrix of a number of variables has all its latent roots equal, except one, then the 'principal component' or latent vector corresponding to this 'anomalous' root can be called the single 'non-isotropic' component because if this component is removed, the variation in any other orthogonal direction is isotropic. In geometrical language, all the principal axes of the familiar ellipsoid (given by the exponent in the density function of a multivariate normal distribution), except one, are equal; in other words, the ellipsoid does not degenerate into a sphere because of this exceptional principal axis. Such a situation can arise in factor-analysis if there is only one 'common' factor (for details see ? 2) besides the 'specific' factor in the factor-structure. If, therefore, we are testing the adequacy of a single hypothetical non-isotropic principal component, it is necessary-as in the case of 'external' analysis-to consider the following two aspects: (i) departure from the hypothesis due to there being more than one non-isotropic principal components, and (ii) departure due to deviation in direction of the true principal component from the hypothetical one. In ? 2 of this paper, these two aspects are considered and an over-all x2 test is obtained, and the underlying assumptions are stated clearly. In ? 3, the over-all X2 iS partitioned and its 'direction' part Ad is separated, using a geometrical argument similar to the one used by Bartlett (1951 a) in deriving the 'direction factor' in external analysis. In ? 4. A is expressed in terms of rectangular co-ordinates. In ? 5, %d is expressed in terms of the sample latent roots and principal components in a manner similar to that of Williams (1955). This is also alternatively expressed in terms of 'residual' roots of the sample variance-covariance matrix, following Williams's (1952) idea of 'residual roots'. In ? 6, the problem of the distribution of these residual roots is considered; and finally in ? 7, the theory is illustrated by a numerical example and a method of deriving approximate confidence intervals for the elements of the single non-isotropic component is described and illustrated.

Theoretical Considerations Concerning theD+DReactions

Some possibilities are explored for the theoretical explanation of the angular distribution of $D+D$ reaction products. The variation with energy is ascribed entirely to differences in the centrifugal barriers encountered by the bombarding particles responsible for the isotropic and non-isotropic components. The detailed data on the proton distributions at low energies appear to be explained in terms of an asymmetric part produced by $P$-waves superposed on isotropic emissions caused by $S$-waves. However, ordinary extrapolation of this to higher energies gives much less symmetric distributions than experimentally found at such energies for the emission of neutrons. If the experiments are correct as interpreted, then they appear to show that spin-orbit coupling plays a large part in the reactions. In that case, an isotropic component produced by incoming $P$-waves grows in importance with energy and accounts for the increasingly parallel growth of the isotropic and asymmetric emissions.