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At least 73 records · Page 4

Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results

Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.

Petersen, Walter A.↗

The effect of wave-particle interactions on the polar wind: Preliminary results

A Monte Carlo simulation was developed in order to study the effects of wave-particle interactions (WPI) on the plasma outflow in the polar wind. The simulation also considered the other mechanisms included in the `classical' polar wind studies such as gravity, the polarization electrostatic field, and the divergence of geomagnetic field lines. Although the plasma consisted of electrons, H(+) and O(+) ions, we emphasized the behavior of H(+) in this preliminary study. The ion distribution function, as well as the profiles of its moments (density, drift velocity, temperatures, etc.) were found for different levels of WPI, that is, for different values of normalized diffusion rates in the velocity space (normalized D(sub perpendicular) H(+)). We found that as the WPI strength increases: (1) the ion drift velocity increases and its density decreases; (2) the perpendicular temperature T(sub perpendicular) (H(+)) increases; (3) the parallel temperature T(sub parallel) (H(+)) first decreases and then increases due to the balance between the parallel adiabatic cooling and the transfer of the energy from the perpendicular to the parallel direction; and (4) the temperature anisotropy ((T(sub parallel) (H(+))/T(sub perpendicular) (H(+)) is reduced and even reversed in some cases. For strong WPI (normalized D(sub perpendicular) (H(+) much greater than 1), the ion distribution function shows weak conic features at high altitudes.

Barakat, A. R.↗

Vibration computer programs E13101, E13102, E13104, and E13112 and application to the NERVA program. Project 187: Methodology documentation

Programs for the analyses of the free or forced, undamped vibrations of one or two elastically-coupled lumped parameter teams are presented. Bearing nonlinearities, casing and rotor distributed mass and elasticity, rotor imbalance, forcing functions, gyroscopic moments, rotary inertia, and shear and flexural deformations are all included in the system dynamics analysis. All bearings have nonlinear load displacement characteristics, the solution is achieved by iteration. Rotor imbalances allowed by such considerations as pilot tolerances and runouts as well as bearing clearances (allowing concail or cylindrical whirl) determine the forcing function magnitudes. The computer programs first obtain a solution wherein the bearings are treated as linear springs of given spring rates. Then, based upon the computed bearing reactions, new spring rates are predicted and another solution of the modified system is made. The iteration is continued until the changes to bearing spring rates and bearing reactions become negligibly small.

Mironenko, G.↗

A multi-dimensional kinetic-based upwind solver for the Euler equations

A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.

Eppard, W. M.↗

Resolution requirements for velocity gradients in turbulence

Since high resolution numerical simulations of turbulent flows, or experiments at high Reynolds numbers, represent a substantial investment in resources, the estimation of the minimum resolution required for the study of a given property has been the subject of continued interest. Different properties require, in general, different resolutions, and the present paper is dedicated to the requirements for the measurement of the probability distribution functions of the velocity gradients and, in particular, of their low order moments. The deviation of these quantities from the values corresponding to a Gaussian distribution was one of the first indications of the presence of Reynolds number-dependent intermittency and has been the object of recent interest as numerical simulations have become able to explore the distribution of gradients in the low Reynolds number range, while new experiments have extended the range to increasingly high Reynolds numbers. We will use progressive filtering of the results of numerical simulations of isotropic turbulence as a model for the effect of a sensor of finite size. The numerical issues will be addressed first to ensure that the simulations are fully resolved from the point of view of the velocity gradients. This will also give us an estimate for the numerical resolution required for the different quantities.

Jimenez, Javier↗

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

Deshpande, S. M.↗

Statistics of primordial density perturbations from discrete seed masses

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.

Scherrer, Robert J.↗

TRO-2D - A code for rational transonic aerodynamic optimization

Features and sample applications of the transonic rational optimization (TRO-2D) code are outlined. TRO-2D includes the airfoil analysis code FLO-36, the CONMIN optimization code and a rational approach to defining aero-function shapes for geometry modification. The program is part of an effort to develop an aerodynamically smart optimizer that will simplify and shorten the design process. The user has a selection of drag minimization and associated minimum lift, moment, and the pressure distribution, a choice among 14 resident aero-function shapes, and options on aerodynamic and geometric constraints. Design variables such as the angle of attack, leading edge radius and camber, shock strength and movement, supersonic pressure plateau control, etc., are discussed. The results of calculations of a reduced leading edge camber transonic airfoil and an airfoil with a natural laminar flow are provided, showing that only four design variables need be specified to obtain satisfactory results.

Davis, W. H., Jr.↗

Principal Effects of Axial Load on Moment-Distribution Analysis of Rigid Structures

This thesis presents the method of moment distribution modified to include the effect of axial load upon the bending moments. This modification makes it possible to analyze accurately complex structures, such as rigid fuselage trusses, that heretofore had to be analyzed by approximate formulas and empirical rules. The method is simple enough to be practicable even for complex structures, and it gives a means of analysis for continuous beams that is simpler than the extended three-moment equation now in common use. When the effect of axial load is included, it is found that the basic principles of moment distribution remain unchanged, the only difference being that the factors used, instead of being constants for a given member, become functions of the axial load. Formulas have been developed for these factors, and curves plotted so that their applications requires no more work than moment distribution without axial load. Simple problems have been included to illustrate the use of the curves.

James, Benjamin Wylie↗

Spatial analysis of storm depths from an Arizona raingage network

Eight years of summer rainstorm observations are analyzed by a dense network of 93 raingages operated by the U.S. Department of Agriculture, Agricultural Research Service, in the 150 km Walnut Gulch experimental catchment near Tucson, Arizona. Storms are defined by the total depths collected at each raingage during the noon-to-noon period for which there was depth recorded at any of the gages. For each of the resulting 428 storm days, the gage depths are interpolated onto a dense grid and the resulting random field analyzed to obtain moments, isohyetal plots, spatial correlation function, variance function, and the spatial distribution of storm depth.

Fennessey, N. M.↗

Application of spatial Poisson process models to air mass thunderstorm rainfall

Eight years of summer storm rainfall observations from 93 stations in and around the 154 sq km Walnut Gulch catchment of the Agricultural Research Service, U.S. Department of Agriculture, in Arizona are processed to yield the total station depths of 428 storms. Statistical analysis of these random fields yields the first two moments, the spatial correlation and variance functions, and the spatial distribution of total rainfall for each storm. The absolute and relative worth of three Poisson models are evaluated by comparing their prediction of the spatial distribution of storm rainfall with observations from the second half of the sample. The effect of interstorm parameter variation is examined.

Eagleson, P. S.↗

What does Reflection from Cloud Sides tell us about Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from CloudSat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3-D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimentional(3-D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 microns) and one with liquid water efficient absorption of solar radiation (2.1 microns). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3-D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, A.↗

What Does Reflection from Cloud Sides Tell Us About Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from Cloudsat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimensional (3D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 micrometers) and one with liquid water efficient absorption of solar radiation (2.1 micrometers). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, Alexander↗

A dipole moment of the microwave background as a cosmological effect

A spherically symmetrical Tolman-Bondi cosmological model is presented in which the curvature of space and the entropy variety with distance from the center. The dipole and quadrupole moments in the distribution of the microwave background radiation are calculated as a function of cosmic time and position of an observer, assuming that the distance to the horizon is much smaller than any characteristic scale in the model. The quadrupole moment is found to be affected mostly by the gradient in the curvature of space while the dipole moment is dominated by the gradient of entropy. The results indicate that the observed dipole in the microwave background may be cosmological in origin. Observational tests of this argument are suggested.

Paczynski, Bohdan↗

The effect of wave-particle interactions on the polar winds O(+)

The escape of the polar wind plasma is an important element in the ionosphere-magnetosphere coupling. Both theory and observations indicate that the wave-particle interactions (WPI) play a significant role in the dynamics of ion outflow along open geomagnetic field lines. A Monte Carlo simulation was developed in order to include the effect of the WPI in addition to the factors that are traditionally included in the 'classical' polar wind (i.e. gravity, electrostatic field, and divergence of geomagnetic field lines). The ion distribution function (f(sub j)), as well as the profiles of its moments (density, drift velocity, temperature, etc.) were found for different levels of WPI, that is, for different values of the normalized diffusion rate in the velocity space (D(tilde) (sub j perpendicular). Although the model included O(=), H(+) and eletrons, we presented only the results related to the O(+) ion. We found that (1) both the density and drift velocity of O(+) increased with the WPI strength, and consequently, the O(+) escape flux was enhanced by a factor of up to 10(exp 5), (2) The O(+) ions could be energized up to a few electron volts; (3) for moderate and high levels of WPI D(tilde) (sub perpendicular) (O(+) greater than (tilde) 1, the distribution function f(O(+)) displayed very pronounced conic features at altitudes around 3 R(sub e). Finally, the interplay between the downward body force, the upward mirror force, and the perpendicular heating resulted in the formation of the 'pressure cooker' effect. This phenomena explained some interesting features of our solution, such as, the peak in the O(=) temperature, and the formation of 'ears' and conics for f(O(+)) around 2.5 R(sub e).

Barakat, A. R.↗

Theoretical Calculation of the Power Spectra of the Rolling and Yawing Moments on a Wing in Random Turbulence

The correlation functions and power spectra of the rolling and yawing moments on an airplane wing due to the three components of continuous random turbulence are calculated. The rolling moments to the longitudinal (horizontal) and normal (vertical) components depend on the spanwise distributions of instantaneous gust intensity, which are taken into account by using the inherent properties of symmetry of isotropic turbulence. The results consist of expressions for correlation functions or spectra of the rolling moment in terms of the point correlation functions of the two components of turbulence. Specific numerical calculations are made for a pair of correlation functions given by simple analytic expressions which fit available experimental data quite well. Calculations are made for four lift distributions. Comparison is made with the results of previous analyses which assumed random turbulence along the flight path and linear variations of gust velocity across the span.

Eggleston, John M↗

Kinetic and thermodynamic properties of a convecting plasma in a two-dimensional dipole field

Charged particle guiding center motion is considered in the magnetic field of a two-dimensional ('line') dipole on which is superimposed a small, static, perpendicular electric field. The parallel equation of motion is that of a simple harmonic oscillator for cos theta, the cosine of magnetic colatitude theta. Equations for the perpendicular electric and magnetic drifts are derived as well as their bounce-averaged forms. The latter are solved to yield a bounce-averaged guiding center trajectory, which is the same as that obtained from conversation of magnetic moment mu, longitudinal invariant J, and total (kinetic plus electrostatic) energy K. The algebraic simplicity of the trajectory equations is also manifest in the forms of the invariants. An interesting result is that guiding centers drift in such a way that they preserve the values of their equatorial pitch angles and (equivalently) mirror latitudes. The most general Maxwellian form of the equilibrium one-particle distribution function f is constructed from the invariants, and spatially varying density and pressure moments, parallel and perpendicular to the magnetic field, are identified. Much of the paper deals with the more restricted problem in which f is specified as a bi-Maxwellian over a straight line of finite length in the equatorial plane of the dipole and perpendicular to field lines. This might be thought of as specifying a cross-tail ion injection source; our formalism then describes the subsequent spatial development. The distribution away from the source is a scaled bi-Maxwellian but one that is cut off at large and small kinetic energies, which depend on position. Density and pressure components are reduced from the values they would have if the total content of individual flux tubes convected intact. The equatorial and meridional variations of density and pressure components are examined and compared systematically for the isotropic and highly anisotropic situations. There appears to be little qualitative difference due to anisotropy. An anisotropy measure is defined, and its spatial variation determined as a signature of possible MHD instability. Extreme values are found, larger than at the source, but the plasma beta in such regions is probably so low as to render the effect inconsequential energetically. Finally, the possible consequence of 'nonadia- batic' pressure profiles on electrostatic interchanges is considered, and a boundary delineating stabilizing and destabilizing regions determined.

Huang, T. S.↗

Kinetic theory analysis of rarefied gas flow through finite length slots

An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.

Raghuraman, P.↗