Local isotropy in turbulent shear flow
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Corrsin, Stanley↗
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Satellite test of the isotropy of the one-way spe ed of light using ExTRAS
A test of the second postulate of special relativity, the universality of the speed of light, using the ExTRAS (Experiment on Timing Ranging and Atmospheric Sounding) payload to be flown on board a Russian Meteor-3M satellite (launch date January 1997) is proposed. The propagation time of a light signal transmitted from one point to another without reflection would be measured directly by comparing the phases of two hydrogen maser clocks, one on board and one on the ground, using laser or microwave time transfer systems. An estimated uncertainty budget of the proposed measurements is given, resulting in an expected sensitivity of the experiment of delta c/c is less than 8xl0(exp -10) which would be an improvement by a factor of approximately 430 over previous direct measurements and by a factor of approximately 4 over the best indirect measurement. The proposed test would require no equipment additional to what is already planned and so is of inherently low-cost. It could be carried out by anyone having access to a laser or microwave ground station and a hydrogen maser.
Wolf, Peter↗
Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability
The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.
Lallemand, Pierre↗
Pitch Angle Isotropy of Relativistic Electron Microbursts as Observed by SAMPEX/HILT: Statistical and Storm‐Time Properties
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Conrad Meyer‐Reed↗
Local anisotropy in strained turbulence at high Reynolds numbers
It is shown that the hypothesis of local isotropy is implausible in the presence of significant mean rates of strain. In fact, it appears that in uniform shear flow near equilibrium, local isotropy can never constitute a systematic approximation, even in the limit of infinite Reynolds number. An estimate of the level of mean strain rate for which local isotropy is formally a good approximation is provided.
Durbin, P. A.↗
Remarks on the nature of gamma-ray bursts
We first recall that in radio astronomy, isotropy and source counts steeper than the Euclidean value of -1.5 provided early evidence for the cosmological nature of radio sources. We discuss briefly whether anything can be wrong with the evidence for isotropy and a nonuniform distribution of GRBs. We identify the selection of cosmic GRBs among recorded bursts and their isotropy as the weaker part of the evidence. We suggest a way to relate the various V/V(max) values to each other. We point out that the strong concentration of small V/V(max) values fits well with a uniform distribution of sources out to a redshift of about 2, but note that sources observed at these redshifts generally exhibit evolution, i.e., a nonuniform space distribution.
Schmidt, Maarten↗
Effects of location uncertainties on the observed distribution of gamma-ray bursts detected by BATSE
The Burst and Transient Source Experiment (BATSE) on NASA's Compton Gamma-Ray Observatory has shown that the sources of gamma-ray bursts have an angular distribution consistent with isotropy, yet the bursts are spatially inhomogeneous. Detection of a statistically significant deviation from isotropy in the burst distribution would provide a clue to the distance of the burst sources. BATSE's ability to detect slight deviations of the angular distribution from isotropy is, in part, dependent on the accuracy of the computed burst locations. Using bursts whose locations have been determined accurately and independently, we estimate BATSE's location uncertainties and incorporate them into 3D Monte Carlo simulations of the burst distributions to show that, despite individual burst location uncertainties of about 5 deg, the ability of BATSE to place stringent limits on the anisotropy present in the angular distribution of the gamma-ray bursts is not significantly degraded. Observational effects of possible galactic halo distributions of the burst sources are noted.
Horack, J. M.↗
Small-scale behavior in distorted turbulent boundary layers at low Reynolds number
During the last three years we have conducted high- and low-Reynolds-number experiments, including hot-wire measurements of the velocity fluctuations, in the test-section-ceiling boundary layer of the 80- by 120-foot Full-Scale Aerodynamics Facility at NASA Ames Research Center, to test the local-isotropy predictions of Kolmogorov's universal equilibrium theory. This hypothesis, which states that at sufficiently high Reynolds numbers the small-scale structures of turbulent motions are independent of large-scale structures and mean deformations, has been used in theoretical studies of turbulence and computational methods such as large-eddy simulation; however, its range of validity in shear flows has been a subject of controversy. The present experiments were planned to enhance our understanding of the local-isotropy hypothesis. Our experiments were divided into two sets. First, measurements were taken at different Reynolds numbers in a plane boundary layer, which is a 'simple' shear flow. Second, experiments were designed to address this question: will our criteria for the existence of local isotropy hold for 'complex' nonequilibrium flows in which extra rates of mean strain are added to the basic mean shear?
Saddoughi, Seyed G.↗
On the Universality of the Kolmogorov Constant in Numerical Simulations of Turbulence
Motivated by a recent survey of experimental data, we examine data on the Kolmogorov spectrum constant in numerical simulations of isotropic turbulence, using results both from previous studies and from new direct numerical simulations over a range of Reynolds numbers (up to 240 on the Taylor scale) at grid resolutions up to 512(exp 3). It is noted that in addition to k(exp -5/3) scaling, identification of a true inertial range requires spectral isotropy in the same wavenumber range. We found that a plateau in the compensated three-dimensional energy spectrum at k(eta) approx. = 0.1 - -0.2, commonly used to infer the Kolmogorov constant from the compensated three-dimensional energy spectrum, actually does not represent proper inertial range behavior. Rather, a proper, if still approximate, inertial range emerges at k(eta) approx. = 0.02 - 0.05 when R(sub lambda) increases beyond 140. The new simulations indicate proportionality constants C(sub 1) and C in the one- and three-dimensional energy spectra respectively about 0.60 and 1.62. If the turbulence were perfectly isotropic then use of isotropy relations in wavenumber space (C(sub 1) = 18/55 C) would imply that C(sub 1) approx. = 0.53 for C = 1.62, in excellent agreement with experiments. However the one- and three-dimensional estimates are not fully consistent, because of departures (due to numerical and statistical limitations) from isotropy of the computed spectra at low wavenumbers. The inertial scaling of structure functions in physical space is briefly addressed. Since DNS is still restricted to moderate Reynolds numbers, an accurate evaluation of the Kolmogorov constant is very difficult. We focus on providing new insights on the interpretation of Kolmogorov 1941 similarity in the DNS literature and do not consider issues pertaining to the refined similarity hypotheses of Kolmogorov (K62).
Yeung, P. K.↗
The UCSD/MIT hard X-ray and low energy gamma ray experiment for HEAO-A
An HEAO-A spacecraft is described which is scheduled for launch in April 1977 to survey the sky in the 0.15 keV to 10 MeV range of X-rays with improved sensitivity and angular resolution. The spectral and time variations of discrete sources, and the spectrum and isotropy of the diffuse component will be measured. A hard X-ray and low energy gamma ray experiment is described which will use as an array of seven (NaI)(Tl)/CsI(Na) phoswich detectors and eight large CsI(Na) shields. Detector events are pulse-height analyzed with a selectable time resolution of 0.1, 0.005, or 0.00002 sec. The instrument background is expected to be comprised of approximately equal parts of diffuse gamma rays entering the aperture, radioactive decay of spallation products, and gamma ray leakage through the shields. Detailed background predictions are presented, and sensitivity estimates indicate that the Crab nebula should be detected up to approximately 5 MeV. Approximate 1% isotropy limits for the diffuse component of cosmic gamma rays should be achieved, and its spectrum measured with improved precision.
Matteson, J. L.↗
Compton and synchrotron processes in spherically-symmetric non-thermal sources
A framework is developed for the accurate calculation of Compton and synchrotron processes in a special class of spherically-symmetric sources. The models considered take a distribution in magnetic field values and high-energy electron density that varies smoothly from central values to values at the outer boundary of the source. Further, the assumption is made that the magnetic field has local disorder (isotropy) and the high-energy electron distribution has local isotropy. Then, in terms of parameters of the source, the synchrotron brightness distribution, total synchrotron flux, Compton-synchrotron flux, and synchrotron self-absorption turnover are all computed accurately. Results are given with a view toward application to the analysis of compact non-thermal sources.
Gould, R. J.↗
Estimating three-demensional energy transfer in isotropic turbulence
To obtain an estimate of the spectral transfer function that indicates the rate of decay of energy, an x-wire probe was set at a fixed position, and two single wire probes were set at a number of locations in the same plane perpendicular to the mean flow in the wind tunnel. The locations of the single wire probes are determined by pseudo-random numbers (Monte Carlo). Second order spectra and cross spectra are estimated. The assumption of isotropy relative to second order spectra is examined. Third order spectra are also estimated corresponding to the positions specified. A Monte Carlo Fourier transformation of the downstream bispectra corresponding to integration across the plane perpendicular to the flow is carried out assuming isotropy. Further integration is carried out over spherical energy shells.
Li, K. S.↗
Pulsations in magnetic field and ion flux observed at L = 4.5 on August 5, 1972
Observations made from space (Explorer 45) near L = 4.5 and from magnetic observatories on the ground of the large-amplitude ULF pulsations that followed the unusually strong compression of the earth's magnetosphere associated with the geomagnetic storm of August 1972 are analyzed. A spectral analysis of Explorer 45 magnetometer data indicates a compressional mode oscillation coupled to a transverse mode oscillation. Enhancements in amplitude of a 300-s period wave near 0040 UT August 5 are found to coincide with an intensification of 100- to 1000-Hz magnetic and electric field oscillations and with the appearance of fluxes of energetic ions. It is noted that during this period the ion pitch angle distribution in each available energy channel (24-300 keV) followed a periodic sequence, apparently synchronized with the magnetic pulsations, from normal trapping (highest fluxes near 90 deg and lowest near 0 deg and 180 deg) to a nearly isotropic particle distribution. It is found that during the transitions the particle flux near 90 deg pitch angle was alternately large earthward of the satellite (before isotropy) and larger radially outward from the satellite (after isotropy).
Engebretson, M. J.↗
Origin and anisotropy of the cosmic submillimeter background
Some cosmological implications of the recently discovered submillimeter background (SMB) are discussed. Opacity and isotropy arguments show that if the background is due to dust emission it must originate at a high redshift z greater than about 10. Isotropy measurements are used to constrain the amplitude of dust optical-depth fluctuations and hence the scale of dust inhomogeneity. The observed flux, the inferred high z and high opacity imply that on small scales the mock gravitational instability driven by radiation pressure may have dominated gravitational effects.
Hogan, C. J.↗
Scatterometer azimuthal response and wind wave directionality
Azimuthal response of a scatterometer to radiation scattered by the sea surface was studied in a wind-wave tank. The variation of the normalized radar cross section with the azimuth angle is fitted by a three-term series. Results show that the upwind-downwind asymmetry decreases as the wind speed increases. The crosswind modulation depends on the wind velocity. The results show that the evolution of the long-wind-crosswind ratio evolves with wind speed in a manner similar to the evolution of the isotropy of short capillary-gravity waves. The maximum of the isotropy of the short wind waves is obtained for wind velocities close to 4 m/s. For the same value of the velocity, the variations of radar response between long-wind and crosswind directions is minimum. For lower or higher values of wind velocities the directional accuracy of the radar increases, since the wind-wave field tends to align in the wind direction.
Giovanangeli, J. P.↗
A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
Shih, Tsan-Hsing↗
Renormalization group analysis of the Reynolds stress transport equation
The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.
Rubinstein, R.↗
Some characteristics of small-scale turbulence in a turbulent duct flow
The fine-scale structure of turbulence in a fully developed turbulent duct flow is examined by considering the 3D velocity derivative field obtained from direct numerical simulations at two relatively small Reynolds numbers. The magnitudes of all mean-square derivatives (normalized by wall variables) increase with the Reynolds number, the increase being largest at the wall. These magnitudes are not consistent with the assumption of local isotropy except perhaps near the duct center-line. When the assumption of local isotropy is relaxed to one of local axisymmetry, or invariance with respect to rotation about a coordinate axis (here chosen in the streamwise direction), satisfactory agreement is indicated by the data outside the wall region. Support for axisymmetry is demonstrated by anisotropy invariant maps of the dissipation and vorticity tensors.
Antonia, R. A.↗