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NASA NTRS1982

Focusing of waves in turbulent inhomogeneous media

A stochastic method using geometrical acoustics is employed to investigate the growth of a large fluctuation in the amplitude of high-frequency waves or shocks propagating through turbulent, inhomogeneous media. Nonlinear terms are retained in the analysis to correctly model focusing and growth of singular fluctuations in the amplitude. A two-dimensional analysis reveals that fluctuations in the ray-tube area grow exponentially and every ray displays caustics. Probability densities for the appearance of caustics are provided, and moments of the ray-tube area distribution and amplitude-related statistics are formulated for distances far into the region of caustic formation. Finally, a relationship is defined between theoretical predictions and measurements on an image plane.

Kulkarny, V. A.↗
NASA NTRS1985

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Balas, M. J.↗
NASA NTRS1994

The Theta-z relation for HST bulges and disks out to z approximately equal 0.8

We present Hubble Space Telescope (HST) scale lengths and ground-based redshifts for 63 faint field galaxies down to I less than or approximately 21.5 mag from the Medium-Deep Survey. These have measured redshifts z less than or approximately 0.8 and half-light radii 0.1 sec less than or approximately r(sub e), r(sub s) less than or approximately 5 sec. We present the Theta-z relation for r(exp 1/4)-bulges and exponential disks separately for world models with q(sub 0) = 0.0-1.0. We show that selection against low surface brightness galaxies in the HST images and ground-based spectra is comparable to that in local surveys. We compare our HST disk-dominated galaxies to a magnitude-limited subsample of the European Southern Observatory (ESO)-Uppsala local spirals. Extrapolating the best-fit local exponential disk scale length (r(sub s) = 3.5 kpc for H(sub 0) = 75) out to z = 0.8, we find a rather symmetrical distribution of HST disks around this value. This implies that galaxy disks have been stable since z is approximately equal to 0.8. We compare our HST bulge-dominated galaxies with r(exp 1/4)-profiles to a magnitude-limited subsample of local Seven Samurai ellipticals. The latter have a local best fit r(sub e) = 5.7 kpc. Our HST bulge sample shows a similar distribution for z less than or approximately 0.8. Elliptical galaxy scale lengths have thus also remained rather constant since z less than or approximately 0.8. We set limits to their possible evolution.

Mutz, Steven B.↗
NASA NTRS2013

Hubble Space Telescope Hx Imaging of Star-forming Galaxies at z approximately equal to 1-1.5: Evolution in the Size and Luminosity of Giant H II Regions

We present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Hα emission in a sample of eight gravitationally lensed galaxies at z = 1-1.5. The magnification caused by the foreground clusters enables us to obtain a median source plane spatial resolution of 360 pc, as well as providing magnifications in flux ranging from approximately 10× to approximately 50×. This enables us to identify resolved star-forming HII regions at this epoch and therefore study their Hα luminosity distributions for comparisons with equivalent samples at z approximately 2 and in the local Universe. We find evolution in the both luminosity and surface brightness of HII regions with redshift. The distribution of clump properties can be quantified with an HII region luminosity function, which can be fit by a power law with an exponential break at some cut-off, and we find that the cut-off evolves with redshift. We therefore conclude that 'clumpy' galaxies are seen at high redshift because of the evolution of the cut-off mass; the galaxies themselves follow similar scaling relations to those at z = 0, but their HII regions are larger and brighter and thus appear as clumps which dominate the morphology of the galaxy. A simple theoretical argument based on gas collapsing on scales of the Jeans mass in a marginally unstable disc shows that the clumpy morphologies of high-z galaxies are driven by the competing effects of higher gas fractions causing perturbations on larger scales, partially compensated by higher epicyclic frequencies which stabilize the disc.

H imaging↗
NASA NTRS1990

Numerical simulations of the decay of Martian global dust storms

The decay of Martian global (great) dust storms is investigated. One-dimensional (vertical, static atmosphere) and two-dimensional (latitude-height, steady state circulation) simulations carried out with an aerosol transport-microphysical model indicate that atmospheric motions play a significant role in the observed decay of global dust storms. Spacecraft observations (Mariner 9, Viking) of the 1971 and the two 1977 planet-encircling dust storms have provided suggestions about some characteristics of storm decay. Specifically, the dust particle size distribution is inferred to have remained essentially unchanged for particles with radii between 1 and 10 microns during decay of the 1971 storm, and surface visible opacity declined quasi-exponentially with time in northern midlatitudes during the decay of the two 1977 storms. The results from this investigation indicate that two- and three-dimensional dynamical processes play a significant role the observed decay features of Martian global dust storms. The most important processes are the lofting of dust by vertical motions in the dust source region of the Southern Hemisphere subtropics and a continuing advective resupply of atmospheric dust into the dust sink regions of the Northern Hemisphere. This work has implications for Viking data analyses and future Mars observer observations and requires that the particle size distribution be treated as a time and latitude dependent quantity.

Murphy, James R.↗
NASA NTRS2019

Lightning Strike Distance Distribution Beyond a Preexisting Lightning Area

The 45th Weather Squadron (45 WS) asked the Applied Meteorology Unit (AMU) to review the 30-year-old, lightning stand-off distances of 5 nautical miles (nmi) for applicability to today's operations. This was based on the realization that previous lightning strike distance studies did not match how 45 WS issues lightning warnings (Roeder, 2008). The previous lightning distance studies were from the point of origin of the lightning or the average starting location that would tend to be in the core of the thunderstorm. However, the 45 WS issues lightning warnings based on the edge of a preexisting lightning area. Before beginning the AMU project, it took several years to develop a method to calculate a distance distribution beyond a preexisting area (Roeder, 2015). The AMU pulled Lightning Detection and Ranging (LDAR) sensor data from 1/1/2013 to 12/31/2013. This dataset consisted of 37 million individual source data points from the LDAR sensors. Only sources within 50 km north, south, east or west of the LDAR grid center were included in the dataset. This limited the use of LDAR data to that with the greatest accuracy of source detection and increased data processing. Points were grouped into flashes based on spatial and temporal criteria. Based on the sensitivity analysis the AMU performed on the flash clustering algorithm, a time value of 0.3 seconds was found to model flashes adequately. Distance parameters were tested from 1,500 to 7,500 meters (m) in 500 m increments. Distance parameters of both 3,000 m and 4,000 m produced results in the plotting tool that were most representative of the physical behavior of lightning. Thus statistics were gathered for the most representative of these spatial and temporal criteria on the flash size and the polygon expansion distance in order to find the correct data distributions. The best fit curves for the LDAR polygon expansion frequency vs. distances for both the 3 kilometer (km) and 4 km distance threshold values were exponential decay functions and had R2 values of > 0.998, indicating good model fits. The equations of the best fit curves were then used to calculate a desired safety radius of 4 nmi for either 3 km or 4 km distance threshold criteria. The AMU analysis concludes the safe reduction of the 5 nmi lightning warning circles to 4 nmi should improve the operational impact by 36% if based on distance from the center of the property area being protected. If based on the edge of the property being protected, then the reduction is 4.5 nmi to 4 nmi and the operational impact is decreased by 21%. For the 6 nmi lightning warning circles, the recommended 4 nmi stand-off distance will result in a safe reduction of operational impact of 31% if based on the center of the area being protected, or 16% if based on the edge of the property.

Flash clustering algorithm↗
NASA NTRS1994

Observations of stratospheric hydrogen fluoride by halogen occultation experiment (HALOE)

The Halogen Occultation Experiment (HALOE) Hydrogen Fluoride (HF) channel on the Upper Atmospheric Research Satellite (UARS) is providing the first global measurements of stratospheric HF, the dominant flourine reservoir in the atmosphere. This paper describes the latitudinal and seasonal variations of HALOE-observed HF in terms of vertical profiles, altitude/latitude cross sections, and column abundances. The HF global distribution shows a 'tracerlike' structure and its column amount increases with latitude, in agreement with previous aircraft measurements of the HF column amount. A comparison between the HALOE HF column above 20 km and the ATMOS 1985 measurements is used to estimate the annual rate of increase of stratospheric HF. Exponential rates of 4.9-6.6%/yr and linear growth rates of 6-8.6%/yr in 1985 and 4.3-5.5%/yr in 1992-1993 are found. HALOE HF measurements during the 1993 Antarctic spring are briefly described. This species behaves like a conserved tracer and its distribution shows an area of enhanced mixing ratios correlated with the polar vortex that has a clear latitude boundary. Finally, simulated HF distributions by the National Center for Atmospheric Research (NCAR) two-dimensional model are used to compare with HALOE observations of HF. Reasonable agreements in the global structure and the absolute amount of HF are found. The differences between the model and the observed results indicate the need for improving treatment of atmospheric dynamics and fluorine-related chemical parameters in the model simulations.

Luo, M.↗
NASA NTRS1994

The origin and evolution of short-period Miras in the solar neighborhood: Constraints on the life cycle of old stars

The spatial distribution of the short-period (P less than 300 days) oxygen-rich Miras in the solar neighborhood can be fitted with an exponential scale height above the Galactic plane of about 600 pc. Using the Gliese catalog of local main-sequence stars, we estimate that the density of suitable G-type progenitor dwarfs within 20 pc of the Sun for these short-period Miras is 6 x 10(exp -4)/cu pc. The portion of the H-R diagram near the main-sequence turnoff of these velocity-selected Gliese stars is intermediate between that of the old open cluster NGC 188 and that of the metal-rich globular cluster, 47 Tuc. We infer that the main-sequence progenitors of the short-period Miras have masses near 1.0 solar mass, and we estimate that these Miras have ages approximately 9 x 10(exp 9). We also identify a few old disk red giants in the neighborhood of the Sun. On the basis of very limited information, we estimate that the total amount of mass lost from these stars during their first ascent up the red giant branch is less than or equal to 0.1 solar mass. We derive a duration of the short-period Mira phase of close to 5 x 10(exp 5) yr. This estimate for the duration of the short period Mira phase is longer than our estimate of 2 x 10(exp 5) yr for the duration of the Mira phase for stars with periods longer than 300 days. From their infrared colors, we estimate a typical mass-loss rate from the short-period Miras of approximately 1 x 10(exp -7) solar mass/yr.

Jura, M.↗
NASA NTRS1994

Evolution of Pinatubo aerosol near 19 km altitude over western North America

Stratospheric aerosols, collected near 19 km altitude on wire impactors over western North America from August 20, 1991 to May 11, 1993, show strong influence of the June 1991 Mt. Pinatubo eruption. Lognormal size distributions are bimodal; each of the mode radii increases and reaches maximum value at about 15 months after eruption. The second (large particle) mode becomes well developed then, and about 40% of the droplets are larger than 0.4 micron radius. The eruption of Mt. Spurr (Alaska) may also have contributed to this. Sulfate mass loading decays exponentially (e-folding 216 days), similar to El Chichon. Silicates are present in samples only immediately after eruption. Two years after eruption, sulfate mass loading is about 0.4 micrograms/cu m, about an order of magnitude higher than background pre-volcanic values. Aerosol size distributions are still bimodal with a very well-defined large droplet mode.

Goodman, Jindra↗
NASA NTRS1986

Scattering from mirrors contaminated by particulates - A model

A model has been used to fit the bidirectional reflectance distribution function for a variety of samples with different angles of incidence and degrees of contamination and roughness by the proper adjustment of six parameters. Exponential and Gaussian composite surface height autocorrelation functions are used to simulate the data at the small and medium angles, and a perturbation of these functions with two additional parameters allows the fit of the upward and downward curve portions of the data at the large angles. Good agreement is found with previous results. The present approach is the same as the classical dispersion equation in treating the index of refraction of optical materials.

Wang, Yaujen↗
NASA NTRS1987

Energetic ion and electron phase space densities in the magnetosphere of Uranus

Proton and electron phase space density profiles are constructed from an analysis of Voyager 2 low-energy charged particle data from the magnetosphere of Uranus. The Uranus proton profiles reveal an approximately exponential decline with decreasing radius for L less than about 9 in a relatively dense thermal plasma region with intense plasma wave activity. Among the distributed loss mechanisms at Uranus are satellite sweeping, wave-particle interactions, and charge exchange of protons with an extended hydrogen corona.

Cheng, Andrew F.↗
NASA NTRS1991

Cometary water-group ions in the region surrounding Comet Giacobini-Zinner - Distribution functions and bulk parameter estimates

The bulk parameters (number density and thermal energy density) of cometary water-group ions in the region surrounding Comet Giacobini-Zinner have been derived using data from the EPAS instrument on the ICE spacecraft. The derivation is based on the assumption that the pick-up ion distribution function is isotropic in the frame of the bulk flow, an approximation which has previously been shown to be reasonable within about 400,000 km of the comet nucleus along the spacecraft trajectory. The transition between the pick-up and mass-loaded regions occurs at the cometary shock, which was traversed at a cometocentric distance of about 100,000 km along the spacecraft track. Examination of the ion distribution functions in this region, transformed to the bulk flow frame, indicates the occurrence of a flattened distribution in the vicinity of the local pick-up speed, and a steeply falling tail at speeds above, which may be approximated as an exponential in ion speed.

Staines, K.↗
NASA NTRS1993

High-velocity tails on the velocity distribution of solar wind ions

Recent observations of the solar wind using the SWICS instrument on the Ulysses spacecraft have shown the presence of high-velocity 'tails' on the velocity distribution of protons. Similar features have also been observed on the velocity distributions of helium and oxygen ions. Of the order of 1 percent of the solar wind density is involved in these tails, which are approximately exponential in shape and persist to V = V(B) + 10V(th) or beyond, where VB is the bulk velocity and V(th) the thermal velocity of the solar wind. This paper contains a preliminary description of the phenomenon. It is clear that it is ultimately connected with the passage of interplanetary shocks past the spacecraft and that particle acceleration at oblique shocks is involved.

Ogilvie, K. W.↗
NASA NTRS1988

Recovery of excitation intensity dependence in pulsed, focused beams - Nonsaturated case

It is shown how the dependence of a nonsaturated excitation process on local, instantaneous intensity can be obtained from temporally and spatially unresolved data by inversion, even for a nonuniform intensity distribution in the probe volume. This treatment is in contrast with the usual approach in which effects of nonuniform excitation are either disregarded or simulated. For exponential intensity profiles, the solution is obtained in the form of an Abel inversion. The ill-conditioned nature of the problem is demonstrated, and extension to the study of intensity-dependent line shapes is made.

Ruyten, Wilhelmus M.↗
NASA NTRS1991

Space Shuttle exhausted aluminum oxide - A measured particle size distribution

Aluminum oxide (A2O3) particles were collected from the Space Shuttle exhaust plume immediately following the launch of STS-34 on October 18, 1989. A2O3 samples were obtained at 2.4, 3.0, 3.2, and 7.4 km in altitude. The samples were analyzed using SEM to develope particle size distributions. There were no indications that the particle size distribution changed as a function of altitude. The particle number concentrations per cubic meter of air sampled for the four collections was found to fit an exponential expression.

Cofer, W. R., III↗
NASA NTRS1992

Nonlinear development and secondary instability of large-amplitude Goertler vortices in hypersonic boundary layers

The weakly nonlinear development of large-amplitude Goertler vortices in a small neighborhood of the neutral stability position given by the linear theory is considered. It is shown that if the basic state and the wall curvature satisfy a certain condition, the Goertler vortices will grow until they become so large as to drive a mean flow correction as large as the basic state. Attention is then given to the further downstream evolution of these large-amplitude vortices, and it is shown that the vortices have a triple layer structure which consists of a region of vortex activity bounded by two transition layers over which the amplitude of the harmonic part of the vortex decays to zero exponentially. The positions of the two transition layers are found to be governed by a free boundary problem, which is solved for a number of curvature distribution cases. The secondary instability of the two transition layers is investigated with respect to traveling waves which are pi/2 out of phase in the spanwise direction with the steady Goertler vortices.

Fu, Y.↗
NASA NTRS1999

Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.

Kousen, Kenneth A.↗