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Reduced Dimensionality Analysis of TEMPO Ozone Profile Retrievals Using the Compact Phase Space (CPSR) Algorithm

TEMPO ozone (O 3 ) profile retrievals are expected to have fidelity in the troposphere due the sensitivities of the associated averaging kernels. However, those averaging kernels are severely rank deficiency meaning that a visual inspection of the vertical structure of the averaging kernel profile sensitivities is misleading due linear dependencies in the profile. The Compact Phase Space Retrieval (CPSR) algorithm use singular value decompositions of the averaging kernels and the ‘compressed’ retrieval solution error covariance to project the transformed averaging kernels into a space that removes the linear dependencies and accounts for the solution error uncertainties. In this oral presentation and poster, we apply the CPSR dimensional reduction analysis to TEMPO and TROPOMI O 3 profile retrievals for 13:45 UTC March 29, 2024 to study the phase space characteristics of the transformed averaging kernels as a function of latitude for North America. Our results show that TEMPO generally has more phase space vertical structure in the troposphere than TROPOMI. TEMPO has four to five dominant modes, and TROPOMI has five to six dominant modes. That means that dimensional reduction can reduce the TEMPO resource requirements by ~77% and the TROPOMI requirements by ~81%. Finally, we found that after removing linear dependences and after accounting for solution uncertainties TEMPO still has sensitivities throughout the troposphere.

TEMPO↗

NASA NTRS1974

Theoretical prediction of thick wing and pylon-fuselage-fanpod-nacelle aerodynamic characteristics at subcritical speeds. Part 1: Theory and results

The theoretical development and the comparison of results with data of a thick wing and pylon-fuselage-fanpod-nacelle analysis are presented. The analysis utilizes potential flow theory to compute the surface velocities and pressures, section lift and center of pressure, and the total configuration lift, moment, and vortex drag. The skin friction drag is also estimated in the analysis. The perturbation velocities induced by the wing and pylon, fuselage and fanpod, and nacelle are represented by source and vortex lattices, quadrilateral vortices, and source frustums, respectively. The strengths of these singularities are solved for simultaneously including all interference effects. The wing and pylon planforms, twists, cambers, and thickness distributions, and the fuselage and fanpod geometries can be arbitrary in shape, provided the surface gradients are smooth. The flow through nacelle is assumed to be axisymmetric. An axisymmetric center engine hub can also be included. The pylon and nacelle can be attached to the wing, fuselage, or fanpod.

Tulinius, J. R.↗

NASA NTRS2012

Optimal Initial Perturbations for Ensemble Prediction of the Madden-Julian Oscillation during Boreal Winter

An initialization strategy, tailored to the prediction of the Madden-Julian oscillation (MJO), is evaluated using the Goddard Earth Observing System Model, version 5 (GEOS-5), coupled general circulation model (CGCM). The approach is based on the empirical singular vectors (ESVs) of a reduced-space statistically determined linear approximation of the full nonlinear CGCM. The initial ESV, extracted using 10 years (1990-99) of boreal winter hindcast data, has zonal wind anomalies over the western Indian Ocean, while the final ESV (at a forecast lead time of 10 days) reflects a propagation of the zonal wind anomalies to the east over the Maritime Continent an evolution that is characteristic of the MJO. A new set of ensemble hindcasts are produced for the boreal winter season from 1990 to 1999 in which the leading ESV provides the initial perturbations. The results are compared with those from a set of control hindcasts generated using random perturbations. It is shown that the ESV-based predictions have a systematically higher bivariate correlation skill in predicting the MJO compared to those using the random perturbations. Furthermore, the improvement in the skill depends on the phase of the MJO. The ESV is particularly effective in increasing the forecast skill during those phases of the MJO in which the control has low skill (with correlations increasing by as much as 0.2 at 20 25-day lead times), as well as during those times in which the MJO is weak.

Ham, Yoo-Geun↗

NASA NTRS1993

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

NASA NTRS2002

Scale Dependence of Statistics of Spatially Averaged Rain Rate Seen in TOGA COARE Comparison with Predictions from a Stochastic Model

A characteristic feature of rainfall statistics is that they in general depend on the space and time scales over which rain data are averaged. As a part of an earlier effort to determine the sampling error of satellite rain averages, a space-time model of rainfall statistics was developed to describe the statistics of gridded rain observed in GATE. The model allows one to compute the second moment statistics of space- and time-averaged rain rate which can be fitted to satellite or rain gauge data to determine the four model parameters appearing in the precipitation spectrum - an overall strength parameter, a characteristic length separating the long and short wavelength regimes and a characteristic relaxation time for decay of the autocorrelation of the instantaneous local rain rate and a certain 'fractal' power law exponent. For area-averaged instantaneous rain rate, this exponent governs the power law dependence of these statistics on the averaging length scale $L$ predicted by the model in the limit of small $L$. In particular, the variance of rain rate averaged over an $L \times L$ area exhibits a power law singularity as $L \rightarrow 0$. In the present work the model is used to investigate how the statistics of area-averaged rain rate over the tropical Western Pacific measured with ship borne radar during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean Atmospheric Response Experiment) and gridded on a 2 km grid depends on the size of the spatial averaging scale. Good agreement is found between the data and predictions from the model over a wide range of averaging length scales.

Kundu, Prasun K.↗

NASA NTRS1993

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

Davis, Dominic A. R.↗

NASA NTRS1975

Calculations of unsteady turbulent boundary layers with flow reversal

The results are presented of a series of computational experiments aimed at studying the characteristics of time-dependent turbulent boundary layers with embedded reversed-flow regions. A calculation method developed earlier was extended to boundary layers with reversed flows for this purpose. The calculations were performed for an idealized family of external velocity distributions, and covered a range of degrees of unsteadiness. The results confirmed those of previous studies in demonstrating that the point of flow reversal is nonsingular in a time-dependent boundary layer. A singularity was observed to develop downstream of reversal, under certain conditions, accompanied by the breakdown of the boundary-layer approximations. A tentative hypothesis was advanced in an attempt to predict the appearance of the singularity, and is shown to be consistent with the calculated results.

Nash, J. F.↗

NASA NTRS1994

Influence of cross-flow on nonlinear Tollmien-Schlichting/vortex interaction

The transition of an incompressible three-dimensional boundary layer with strong cross-flow is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two lower-branch Tollmien-Schlichting waves which mutually interact nonlinearly to induce a longitudinal vortex flow. The vortex motion in turn gives rise to significant wave modulation via wall-shear forcing. The characteristic Reynolds number is large and, as a consequence, the waves' and the vortex motion are governed primarily by triple deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Following analysis and computation over a wide range of parameters, three distinct responses are found to emerge in the nonlinear behavior of the flow solution downstream: an algebraic finite-distance singularity, far-downstream saturation or far-downstream wave decay leaving pure vortex flow. These depend on the input conditions, the wave angles and the size of the cross flow.

Davis, D. A. R.↗

NASA NTRS1985

An Overview of Latest Model Reduction and Control Methods of Large Flexible Space Structures

The latest trends and theoretical developments involved with the modeling and control of Large Flexible Space Structures (LFSS) are described. The paper addresses first the basic problems, characteristics, and difficulties inherent in modeling and control of LFSS. Major sources of difficulties and errors are the stiffness and damping operators of the dynamic model. Extensions of Linear Quadratic Gaussian (LQG) theory as applied to LFSS are presented, including frequency-shaped cost functionals and perturbation methods. The minimum data/maximum entropy approach which uses a stochastic design model to overcome difficulties found in the LQG-based methods is described. Latest trends in system theory including balanced realization and singular-value analysis are used to determine reduced order controllers and models. Ad hoc methods such as component cost analysis and modal cost analysis are discussed in context with the closed-loop reduction problem of controller order versus performance. The minimum data/maximum entropy approach also addresses controller order versus performance. Those areas of control science and large scale systems that appear to have an important role in understanding and solving LFSS modeling and control are also identified.

Santiago, J. M.↗

NASA NTRS1993

Matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation for aeroassisted plane-change maneuvers

In this paper we develop a general procedure for constructing a matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is inappropriate since it is not uniformly valid over a narrow range of the independent variable. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished - one where the left boundary condition coincides with or lies to the right of the singular region and one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure, and its potential application to aeroassisted plane change is described.

Calise, Anthony J.↗

NASA NTRS2005

Micromechanics, Fracture Mechanics and Gas Permeability of Composite Laminates for Cryogenic Storage Systems

A micromechanics method is developed to investigate microcrack propagation in a liquid hydrogen composite tank at cryogenic temperature. The unit cell is modeled using square and hexagonal shapes depends on fiber and matrix layout from microscopic images of composite laminates. Periodic boundary conditions are applied to the unit cell. The temperature dependent properties are taken into account in the analysis. The laminate properties estimated by the micromechanics method are compared with empirical solutions using constituent properties. The micro stresses in the fiber and matrix phases based on boundary conditions in laminate level are calculated to predict the formation of microcracks in the matrix. The method is applied to an actual liquid hydrogen storage system. The analysis predicts micro stresses in the matrix phase are large enough to cause microcracks in the composite. Stress singularity of a transverse crack normal to a ply-interface is investigated to predict the fracture behavior at cryogenic conditions using analytical and finite element analysis. When a transverse crack touches a ply-interface of a composite layer with same fiber orientation, the stress singularity is equal to 1/2. When the transverse crack propagates to a stiffer layer normal to the ply-direction, the singularity becomes less than 1/2 and vice versa. Finite element analysis is performed to predict the fracture toughness of a laminated beam subjected to fracture loads measured by four-point bending tests at room and cryogenic temperatures. As results, the fracture load at cryogenic temperature is significantly lower than that at room temperature. However, when thermal stresses are taken into consideration, for both cases of room and cryogenic temperatures, the difference of the fracture toughness becomes insignificant. The result indicates fracture toughness is a characteristic property, which is independent to temperature changes. The experimental analysis is performed to investigate the effect of cryogenic cycling on permeability for various composite material systems. Textile composites have lower permeability than laminated composites even with increasing number of cryogenic cycle. Nano-particles dispersed in laminated composites do not show improvement on permeability. The optical inspection is performed to investigate the microcrack propagation and void content in laminated composites and compared the microscopic results before and after cryogenic cycling.

Choi, Sukjoo↗

NASA NTRS1983

The mechanics of delamination in fiber-reinforced composite materials. Part 2: Delamination behavior and fracture mechanics parameters

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extenstion. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined.

Wang, S. S.↗

NASA NTRS1983

The mechanics of delamination in fiber-reinforced composite materials. II - The delamination behavior and fracture mechanics parameters

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extension. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined. Previously announced in STAR as N84-13222

Wang, S. S.↗

NASA NTRS1990

Theory of finite disturbances in a centrifugal compression system with a vaneless radial diffuser

A previous small perturbation analysis of circumferential waves in circumferential compression systems, assuming inviscid flow, is shown to be consistent with observations that narrow diffusers are more stable than wide ones, when boundary layer displacement effect is included. The Moore-Greitzer analysis for finite strength transients containing both surge and rotating stall in axial machines is adapted for a centrifugal compression system. Under certain assumptions, and except for a new second order swirl, the diffuser velocity field, including resonant singularities, can be carried over from the previous inviscid linear analysis. Nonlinear transient equations are derived and applied in a simple example to show that throttling through a resonant value of flow coefficient must occur in a sudden surge-like drop, accompanied by a transient rotating wave. This inner solution is superseded by an outer surge response on a longer time scale. Surge may occur purely as result of circumferential wave resonance. Numerical results are shown for various parametric choices relating to throttle schedule and the characteristic slope. A number of circumferential modes considered simultaneously is briefly discussed.

Moore, F. K.↗

NASA NTRS1991

Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms

The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.

Lee, Jeh Won↗

NASA NTRS2002

Caustics and Caustic-Interference in Measurements of Contact Angle and Flow Visualization Through Laser Shadowgraphy

As one of the basic elements of the shadowgraphy optical system, the image of the far field from the droplet implicates plentiful information on the droplet profile. An analysis of caustics by wave theory shows that a droplet with a cylindrically symmetric Gaussian-hill-type profile produces a circular directional caustic in far field, which arises from the singularities (inflection line on the surface). The sessile liquid droplets, which profiles are restricted by surface tension, usually have a 'protruding foot' where the surface inflects. Simple geometrical optics indicates that the circular caustic stemming from the surface inflection at the protruding-foot takes the shape of the outmost ring on the image of the far field. It is the diameter of the outmost ring that is used as one of the key parameters in the measurements of contact angle through the laser shadowgraphic method. Different surface characteristics of the droplets produce different type of caustics, and therefore, the shape of the caustics can be used to determine the surface property of the sessile droplets. The present paper describes the measurement method of contact angIe using the circular caustics and the estimation of the protruding-foot height through the caustic interference.

Chao, David F.↗

NASA NTRS1989

Gravitational lensing by a smoothly variable surface mass density

The statistical properties of gravitational lensing due to smooth but nonuniform distributions of matter are considered. It is found that a majority of triple images had a parity characteristic for 'shear-induced' lensing. Almost all cases of triple or multiple imaging were associated with large surface density enhancements, and lensing objects were present between the images. Thus, the observed gravitational lens candidates for which no lensing object has been detected between the images are unlikely to be a result of asymmetric distribution of mass external to the image circle. In a model with smoothly variable surface mass density, moderately and highly amplified images tended to be single rather than multiple. An opposite trend was found in models which had singularities in the surface mass distribution.

Paczynski, Bohdan↗

NASA NTRS2003

Spectral Characteristics of Wake Vortex Sound During Roll-Up

This report presents an analysis of the sound spectra generated by a trailing aircraft vortex during its rolling-up process. The study demonstrates that a rolling-up vortex could produce low frequency (less than 100 Hz) sound with very high intensity (60 dB above threshold of human hearing) at a distance of 200 ft from the vortex core. The spectrum then drops o rapidly thereafter. A rigorous analytical approach has been adopted in this report to derive the spectrum of vortex sound. First, the sound pressure was solved from an alternative treatment of the Lighthill s acoustic analogy approach [1]. After the application of Green s function for free space, a tensor analysis was applied to permit the removal of the source term singularity of the wave equation in the far field. Consequently, the sound pressure is expressed in terms of the retarded time that indicates the time history and spacial distribution of the sound source. The Fourier transformation is then applied to the sound pressure to compute its spectrum. As a result, the Fourier transformation greatly simplifies the expression of the vortex sound pressure involving the retarded time, so that the numerical computation is applicable with ease for axisymmetric line vortices during the rolling-up process. The vortex model assumes that the vortex circulation is proportional to the time and the core radius is a constant. In addition, the velocity profile is assumed to be self-similar along the aircraft flight path, so that a benchmark vortex velocity profile can be devised to obtain a closed form solution, which is then used to validate the numerical calculations for other more realistic vortex profiles for which no closed form solutions are available. The study suggests that acoustic sensors operating at low frequency band could be profitably deployed for detecting the vortex sound during the rolling-up process.

Booth, Earl R., Jr.↗