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NASA NTRS1999

Nonlinear Response of Composite Panels Under Combined Acoustic Excitation and Aerodynamic Pressure

A finite element formulation is presented for the analysis of large deflection response of composite panels subjected to aerodynamic pressure- at supersonic flow and high acoustic excitation. The first-order shear deformation theory is considered for laminated composite plates, and the von Karman nonlinear strain-displacement relations are employed for the analysis of large deflection panel response. The first-order piston theory aerodynamics and the simulated Gaussian white noise are employed for the aerodynamic and acoustic loads, respectively. The nonlinear equations of motion for an arbitrarily laminated composite panel subjected to a combined aerodynamic and acoustic pressures are formulated first in structure node degrees-of-freedom. The system equations are then transformed and reduced to a set of coupled nonlinear equations in modal coordinates. Modal participation is defined and the in-vacuo modes to be retained in the analysis are based on the modal participation values. Numerical results include root mean square values of maximum deflections, deflection and strain response time histories, probability distributions, and power spectrum densities. Results showed that combined acoustic and aerodynamic loads have to be considered for panel analysis and design at high dynamic pressure values.

Abdel-Motagaly, K.↗

NASA NTRS1998

Probabilistic Evaluation of Fuselage-Type Composite Structures

A methodology is developed to simulate computationally the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, natural frequencies, displacements, stress/strain, etc., which are the consequences of the random variation (scatter) of the primitive (independent random) variables in the constituent, plv. laminate and structural levels. This methodology is implemented in a computer code integrated probabilistic assessment of composite structures (IPACS). A fuselage-type composite structure is analyzed to demonstrate the code's capability . The probability distribution functions of the buckling loads, natural frequency, displacement, strain and stress are computed. The sensitivity of each primitive (independent random) variable to a given structural response is also identified from the analyses.

Shiao, Michael C.↗

NASA NTRS1999

Approximation for Horizontal Photon Transport in Cloud Remote Sensing Problems

The effect of horizontal photon transport within real-world clouds can be of consequence to remote sensing problems based on plane-parallel cloud models. An analytic approximation for the root-mean-square horizontal displacement of reflected and transmitted photons relative to the incident cloud-top location is derived from random walk theory. The resulting formula is a function of the average number of photon scatterings, and particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings can be determined from efficient adding/doubling radiative transfer procedures. The approximation is applied to liquid water clouds for typical remote sensing solar spectral bands, involving both conservative and non-conservative scattering. Results compare well with Monte Carlo calculations. Though the emphasis is on horizontal photon transport in terrestrial clouds, the derived approximation is applicable to any multiple scattering plane-parallel radiative transfer problem. The complete horizontal transport probability distribution can be described with an analytic distribution specified by the root-mean-square and average displacement values. However, it is shown empirically that the average displacement can be reasonably inferred from the root-mean-square value. An estimate for the horizontal transport distribution can then be made from the root-mean-square photon displacement alone.

Plantnick, Steven↗

NASA NTRS1997

Evolution of Structure in the Intergalactic Medium and the Nature of the LY-Alpha Forest

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.

Bi, Hongguang↗

NASA NTRS1997

Data Assimilation in the Ocean and in the Atmosphere: What Should be Next?

As part of the International Symposium on Assimilation of Observation in Meteorology and Oceanography, a panel discussion was held on the evening of 15 March 1995. The purpose of this panel discussion was focus on what the next major areas of research in data assimilation should be. The panelists had five minutes each for short presentations (Kalman filters, representers, etc.) and this was followed by an open discussion. This preprocessing will require a good understanding of the fine-scale phenomena. Least square methods such as Kalman filters and variational schemes are inefficient estimators of non-Gaussian field such as chemical traces. Regardless of the modeling technique employed (Lagrangian methods seem best), a least squares assimilation scheme will smear fine structure. The estimator of maximum likelihood must be sought, by examination of tracer probability distributions.

Kalnay, Eugenia↗

NASA NTRS1999

A Probabilistic Approach to Aeropropulsion System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFs) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Tong, Michael T.↗

NASA NTRS2000

Estimating Forest Vertical Structure from Multialtitude, Fixed-Baseline Radar Interferometric and Polarimetric Data

Parameters describing the vertical structure of forests, for example tree height, height-to-base-of-live-crown, underlying topography, and leaf area density, bear on land-surface, biogeochemical, and climate modeling efforts. Single, fixed-baseline interferometric synthetic aperture radar (INSAR) normalized cross-correlations constitute two observations from which to estimate forest vertical structure parameters: Cross-correlation amplitude and phase. Multialtitude INSAR observations increase the effective number of baselines potentially enabling the estimation of a larger set of vertical-structure parameters. Polarimetry and polarimetric interferometry can further extend the observation set. This paper describes the first acquisition of multialtitude INSAR for the purpose of estimating the parameters describing a vegetated land surface. These data were collected over ponderosa pine in central Oregon near longitude and latitude -121 37 25 and 44 29 56. The JPL interferometric TOPSAR system was flown at the standard 8-km altitude, and also at 4-km and 2-km altitudes, in a race track. A reference line including the above coordinates was maintained at 35 deg for both the north-east heading and the return southwest heading, at all altitudes. In addition to the three altitudes for interferometry, one line was flown with full zero-baseline polarimetry at the 8-km altitude. A preliminary analysis of part of the data collected suggests that they are consistent with one of two physical models describing the vegetation: 1) a single-layer, randomly oriented forest volume with a very strong ground return or 2) a multilayered randomly oriented volume; a homogeneous, single-layer model with no ground return cannot account for the multialtitude correlation amplitudes. Below the inconsistency of the data with a single-layer model is followed by analysis scenarios which include either the ground or a layered structure. The ground returns suggested by this preliminary analysis seem too strong to be plausible, but parameters describing a two-layer compare reasonably well to a field-measured probability distribution of tree heights in the area.

Treuhaft, Robert N.↗

NASA NTRS2000

A Probabilistic Approach to Aeropropulsion System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFS) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Tong, Michael T.↗

NASA NTRS2000

On Geomagnetism and Paleomagnetism I

A partial description of Earth's broad scale, core-source magnetic field has been developed and tested three ways. The description features an expected, or mean, spatial magnetic power spectrum that is approximately inversely proportional to horizontal wavenumber atop Earth's core. This multipole spectrum describes a magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Temporal variations of core multipole powers about mean values are to be expected and are described statistically, via trial probability distribution functions, instead of deterministically, via trial solution of closed transport equations. The distributions considered here are closed and neither require nor prohibit magnetic isotropy. The description is therefore applicable to, and tested against, both dipole and low degree non-dipole fields. In Part 1, a physical basis for an expectation spectrum is developed and checked. The description is then combined with main field models of twentieth century satellite and surface geomagnetic field measurements to make testable predictions of the radius of Earth's core. The predicted core radius is 0.7% above the 3480 km seismological value. Partial descriptions of other planetary dipole fields are noted.

Voorhies, Coerte V.↗

NASA NTRS2000

A Geometrical Approach to Bell's Theorem

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

Rubincam, David Parry↗

NASA NTRS2000

Statistics Analysis of the Uncertainties in Cloud Optical Depth Retrievals Caused by Three-Dimensional Radiative Effects

This paper presents a simple approach to estimate the uncertainties that arise in satellite retrievals of cloud optical depth when the retrievals use one-dimensional radiative transfer theory for heterogeneous clouds that have variations in all three dimensions. For the first time, preliminary error bounds are set to estimate the uncertainty of cloud optical depth retrievals. These estimates can help us better understand the nature of uncertainties that three-dimensional effects can introduce into retrievals of this important product of the MODIS instrument. The probability distribution of resulting retrieval errors is examined through theoretical simulations of shortwave cloud reflection for a wide variety of cloud fields. The results are used to illustrate how retrieval uncertainties change with observable and known parameters, such as solar elevation or cloud brightness. Furthermore, the results indicate that a tendency observed in an earlier study, clouds appearing thicker for oblique sun, is indeed caused by three-dimensional radiative effects.

Varnai, Tamas↗

NASA NTRS2000

Airborne Coherent Lidar for Advanced In-Flight Measurements (ACLAIM) Flight Testing of the Lidar Sensor

The purpose of the ACLAIM program is ultimately to establish the viability of light detection and ranging (lidar) as a forward-looking sensor for turbulence. The goals of this flight test are to: 1) demonstrate that the ACLAIM lidar system operates reliably in a flight test environment, 2) measure the performance of the lidar as a function of the aerosol backscatter coefficient (beta), 3) use the lidar system to measure atmospheric turbulence and compare these measurements to onboard gust measurements, and 4) make measurements of the aerosol backscatter coefficient, its probability distribution and spatial distribution. The scope of this paper is to briefly describe the ACLAIM system and present examples of ACLAIM operation in flight, including comparisons with independent measurements of wind gusts, gust-induced normal acceleration, and the derived eddy dissipation rate.

Soreide, David C.↗

NASA NTRS2000

Tropical Convective Outflow and Near Surface Equivalent Potential Temperatures

We use clear sky heating rates to show that convective outflow in the tropics decreases rapidly with height between the 350 K and 360 K potential temperature surfaces (or between roughly 13 and 15 km). There is also a rapid fall-off in the pseudoequivalent potential temperature probability distribution of near surface air parcels between 350 K and 360 K. This suggests that the vertical variation of convective outflow in the upper tropical troposphere is to a large degree determined by the distribution of sub cloud layer entropy.

Folkins, Ian↗

NASA NTRS2000

A Probabilistic Approach to Aeropropulsion System Assessment

Tong, Michael T.↗

NASA NTRS2001

Disturbance Dynamics in Transitional and Turbulent Flows

The dynamics of an ensemble of linear disturbances with a known probability distribution associated with the initial mode amplitudes are studied in boundary-layer flows through an analysis of the transport equations for the mean disturbance kinetic energy and disturbance energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis. Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field in proximity to the wall, the laminar regime fluctuations studied here are influenced across the boundary layer by the solid boundary. In addition to the low Reynolds number, early stage transition regime, the dynamics of these disturbance fields can be related in some respects to the near-wall dynamics of the fully turbulent regime.

Grosch, C. E.↗

NASA NTRS2000

CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets

This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.

Farge, Marie↗

NASA NTRS2000

CVS Filtering of 3D Turbulent Mixing Layers Using Orthogonal Wavelets

Coherent Vortex Simulation (CVS) filtering has been applied to Direct Numerical Simulation (DNS) data of forced and unforced time-developing turbulent mixing layers. CVS filtering splits the turbulent flow into two orthogonal parts, one corresponding to coherent vortices and the other to incoherent background flow. We have shown that the coherent vortices can be represented by few wavelet modes and that these modes are sufficient to reproduce the vorticity probability distribution function (PDF) and the energy spectrum over the entire inertial range. The remaining incoherent background flow is homogeneous, has small amplitude, and is uncorrelated. These results are compared with those obtained for the same compression rate using large eddy simulation (LES) filtering. In contrast to the incoherent background flow of CVS filtering, the LES subgrid scales have a much larger amplitude and are correlated, which makes their statistical modeling more difficult.

Schneider, Kai↗

NASA NTRS2001

Toward a Unified Parameterization of the Boundary Layer and Moist Convection: A New Type of Mass-Flux Model - Part 1

Higher-order closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higher-order moments (e.g., fourth moments in third-order closure models), for pressure terms, and for dissipation terms. Mass-flux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called Assumed-Distribution Higher-Order Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments, thereafter the joint distribution is effectively known, and so any and all moments can be constructed as needed. In this way, the usual closure problem of "higher moments" is avoided. The pressure-term parameterizations previously developed for HOC models are used to predict the convective fluxes and the moments of the vertical velocity. In companion papers, parameterizations of lateral mass exchanges and subplume-scale fluxes are presented, and then ADHOC is applied to several observationally based tropical, subtropical, and dry convective boundary layers.

Lappen, Cara-Lyn↗