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NASA NTRS1984

A modal reduction method for use with nonlinear simulations of flexible multibody spacecraft

This paper presents a modal truncation method that can be used to prepare the structural flexibility data required as input to flexible, multibody spacecraft simulation programs. The method allows one to truncate the structural models of each flexible body in the system such that the assembled system is free of undesired high frequency system modes. This truncation method enables reasonable simulation costs to be incurred while maintaining dynamic simulation fidelity in the frequency range of interest. A simple one-dimensional example is presented which provides a physical interpretation of the method's workings. In addition, results are presented from the application of the method to a complex spacecraft.

Macala, G. A.↗

NASA NTRS1991

The attractor dimension of solar decimetric radio pulsations

The temporal characteristics of decimetric pulsations and related radio emissions during solar flares are analyzed using statistical methods recently developed for nonlinear dynamic systems. The results of the analysis is consistent with earlier reports on low-dimensional attractors of such events and yield a quantitative description of their temporal characteristics and hidden order. The estimated dimensions of typical decimetric pulsations are generally in the range of 3.0 + or - 0.5. Quasi-periodic oscillations and sudden reductions may have dimensions as low as 2. Pulsations of decimetric type IV continua have typically a dimension of about 4.

Kurths, J.↗

NASA NTRS1986

Computer simulations of electromagnetic cool ion beam instabilities

Electromagnetic ion beam instabilities driven by cool ion beams at propagation parallel or antiparallel to a uniform magnetic field are studied using computer simulations. The elements of linear theory applicable to electromagnetic ion beam instabilities and the simulations derived from a one-dimensional hybrid computer code are described. The quasi-linear regime of the right-hand resonant ion beam instability, and the gyrophase bunching of the nonlinear regime of the right-hand resonant and nonresonant instabilities are examined. It is detected that in the quasi-linear regime the instability saturation is due to a reduction in the beam core relative drift speed and an increase in the perpendicular-to-parallel beam temperature; in the nonlinear regime the instabilities saturate when half the initial beam drift kinetic energy density is converted to fluctuating magnetic field energy density.

Gary, S. P.↗

NASA NTRS1994

MHD modeling of magnetotail instability for localized resistivity

We present results of a three-dimensional magnetohydrodynamic (MHD) simulation of magnetotail evolution initiated by a sudden occurrence or increase of spatially localized resistivity as the major expected concequence of some localized microinstability. Because of the absence of a quantitative model, possible variations of resistivity levels with current density, or the reduction thereof, are not incorporated in the present investigation. The emphasis of the study is on an investigation of the changes to the overall evolution brought about by this localization, in particular, on the disruption and diversion of the cross-tail current and the nonlinear evolution of the magnetotail instability. The immediate consequences of the occurrence of the localized resistance and the resulting electric field are a reduction and diversion of the electric current around the region of high resistivity, associated with an increase of B(sub z) ('dipolarization') at the earthward edge and a decrease of B(sub z) at the tailward edge of this region. These effects, however, are localized and do not involve a reduction of the total cross-tail current and hence do not lead to the global development of a 'substorm current wedge,' which includes not only the reduction of the cross-tail current but also the buildup of a global field-aligned current system of 'regional 1' type (toward the Earth on the dawnside and away on the duskside of the tail). Such signatures develop at a later time, as consequences of a three-dimensional tearing instability, which is triggered by the occurrence of the resistivity. These features are found in combination with plasmoid formation and ejection, quite similar to results of earlier simulations with uniform resistivity. Differences are found in the timescale of the evolution, which tends to be shorter for localized resistivity, and in the propagation of the dipolarization effects in the equatorial plane. Whereas for uniform resistivity the temporal increase in B(sub z) tends to propagate tailward, apparently due to a pileup effect in the near-Earth region, an earthward propagation is found for the localized resistivity. This propagation results from an earthward convection of the gradient in B(sub z), which is set up by the reconnection process further tailward.

Hesse, Michael↗

NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The rapid increase in available computational power over the last decade has enabled higher resolution flow simulations and more widespread use of unstructured grid methods for complex geometries. While much of this effort has been focused on steady-state calculations in the aerodynamics community, the need to accurately predict off-design conditions, which may involve substantial amounts of flow separation, points to the need to efficiently simulate unsteady flow fields. Accurate unsteady flow simulations can easily require several orders of magnitude more computational effort than a corresponding steady-state simulation. For this reason, techniques for improving the efficiency of unsteady flow simulations are required in order to make such calculations feasible in the foreseeable future. The purpose of this work is to investigate possible reductions in computer time due to the choice of an efficient time-integration scheme from a series of schemes differing in the order of time-accuracy, and by the use of more efficient techniques to solve the nonlinear equations which arise while using implicit time-integration schemes. This investigation is carried out in the context of a two-dimensional unstructured mesh laminar Navier-Stokes solver.

Jothiprasad, Giridhar↗

NASA NTRS1983

Application of a global variational analysis to quasi three-dimensional temperature retrievals

The Halen and Kalnay (1983) hypothesis that the application of global variational analysis to clear column radiances will result in a reduction of both observational noise and data gaps is tested, together with the hypothesis of these authors that the estimate of clear column radiances furnished by the variational analysis can yield a useful reduction of the data gaps in the retrieved temperatures. In the first of two experiments conducted, attention is given to whether the nonlinearity of the temperature retrieval method is sufficiently strong to result in more accurate temperature retrievals. In the second experiment, realistic subgrid scale cloud fields and observational and temperature errors are included in the simulation system.

Dalcher, A.↗

NASA NTRS2002

Spectral Re-Growth Reduction for CCSDS 8-D 8-PSK TCM

This report presents a study on the CCSDS recommended 8-dimensional 8 PSK Trellis Coded Modulation (TCM) scheme. The important steps of the CCSDS scheme include: conversion of serial data into parallel form, differential encoding, convolutional encoding, constellation mapping, and filtering the 8-PSK symbols using the square root raised cosine (SRRC) pulses. The last step, namely the filtering of the 8 PSK symbols using SRRC pulses, significantly affects the bandwidth of the signal. If a nonlinear power amplifier is used, the SRRC filtered signal creates spectral regrowth. The purpose of this report is to investigate a technique, called the smooth phase interpolated keying (SPIK), that can provide an alternative to SRRC filtering so that good spectral as well as power efficiencies can be obtained with the CCSDS encoder. The results of this study show that the CCSDS encoder does not affect the spectral shape of the SRRC filtered signal or the SPIK signal. When a nonlinear traveling wave tube amplifier (TWTA) is used, the spectral performance of the SRRC signal degrades significantly while the spectral performance of SPIK remains unaffected. The degrading effect of a nonlinear solid state power amplifier (SSPA) on SRRC is found to be less than that due to a nonlinear TWTA. However, in both cases, the spectral performance of the SRRC modulated signal is worse than that of the SPIK signal. The bit error rate (BER) performance of the SRRC signal in a linear amplifier environment is about 2.5 dB better than that of the SPIK signal when both the receivers use algorithms of similar complexity. In a nonlinear TWTA environment, the SRRC signal requires accurate phase tracking since the TWTA introduces additional phase distortion. This problem does not arise with SPIK signal due to its constant envelope property. When a nonlinear amplifier is used, the SRRC method loses nearly 1 dB in the bit error rate performance. The SPIK signal does not lose any performance. Thus the performance gap between SRRC and SPIK reduces. The BER performance of SPIK can be improved even further by using a more optimal receiver. A similar optimal receiver for SRRC is quite complex since the amplifier distorts the pulse shape. However, this requires further investigation and is not covered in this report.

Borah, Deva K.↗

NASA NTRS1978

Investigations of simulated aircraft flight through thunderstorm outflows

The effects of wind shear on aircraft flying through thunderstorm gust fronts were investigated. A computer program was developed to solve the two dimensional, nonlinear equations of aircraft motion, including wind shear. The procedure described and documented accounts for spatial and temporal variations of the aircraft within the flow regime. Analysis of flight paths and control inputs necessary to maintain specified trajectories for aircraft having characteristics of DC-8, B-747, augmentor wing STOL, and DHC-6 aircraft was recorded. From the analysis an attempt was made to find criteria for reduction of the hazards associated with landing through thunderstorm gust fronts.

Frost, W.↗

NASA NTRS1995

Analytical and phenomenological studies of rotating turbulence

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.

Mahalov, Alex↗

NASA NTRS1993

Simulations of ion cyclotron anisotropy instabilities in the terrestrial magnetosheath

Enhanced transverse magnetic fluctuations observed below the proton cyclotron frequency in the terrestrial magnetosheath have been identified as due to the proton cyclotron and helium cyclotron instabilities driven by the T-perpendicular greater than T-parallel condition of the sheath ions. One-dimensional hybrid computer simulations are used here to examine the nonlinear properties of these two growing modes at relatively weak fluctuation energies and for wave vectors parallel to the background magnetic field. Second-order theory predicts fluctuating magnetic field energies at saturation of the proton cyclotron anisotropy instability in semiquantitative agreement with the simulation results. Introduction of the helium component enhances the wave-particle exchange rate for proton anisotropy reduction by that instability, thereby reducing the saturation energy of that mode. The simulations demonstrate that wave-particle interactions by the proton cyclotron and helium cyclotron instabilities lead to the anticorrelation observed by Anderson and Fuselier (1993).

Gary, S. P.↗

NASA NTRS1982

On current aspects of finite element computational fluid mechanics for turbulent flows

A set of nonlinear partial differential equations suitable for the description of a class of turbulent three-dimensional flow fields in select geometries is identified. On the basis of the concept of enforcing a penalty constraint to ensure accurate accounting of ordering effects, a finite element numerical solution algorithm is established for the equation set and the theoretical aspects of accuracy, convergence and stability are identified and quantized. Hypermatrix constructions are used to formulate the reduction of the computational aspects of the theory to practice. The robustness of the algorithm, and the computer program embodiment, have been verified for pertinent flow configurations.

Baker, A. J.↗

NASA NTRS2012

Representation of Probability Density Functions from Orbit Determination using the Particle Filter

Statistical orbit determination enables us to obtain estimates of the state and the statistical information of its region of uncertainty. In order to obtain an accurate representation of the probability density function (PDF) that incorporates higher order statistical information, we propose the use of nonlinear estimation methods such as the Particle Filter. The Particle Filter (PF) is capable of providing a PDF representation of the state estimates whose accuracy is dependent on the number of particles or samples used. For this method to be applicable to real case scenarios, we need a way of accurately representing the PDF in a compressed manner with little information loss. Hence we propose using the Independent Component Analysis (ICA) as a non-Gaussian dimensional reduction method that is capable of maintaining higher order statistical information obtained using the PF. Methods such as the Principal Component Analysis (PCA) are based on utilizing up to second order statistics, hence will not suffice in maintaining maximum information content. Both the PCA and the ICA are applied to two scenarios that involve a highly eccentric orbit with a lower apriori uncertainty covariance and a less eccentric orbit with a higher a priori uncertainty covariance, to illustrate the capability of the ICA in relation to the PCA.

Mashiku, Alinda K.↗

NASA NTRS1994

Nonlinear equilibration of localized instabilities on a baroclinic jet

Dynamical mechanisms underlying the equilibration of absolute instability are examined in a nonlinear, quasigeostrophic, two-layer model. The key to understanding the nonlinear equilibration is in recognizing that linear absolute instabilities can be stabilized both by a reduction of the vertical shear and by enhancement of the mean barotropic velocity. In a localized domain, the equilibration process proceeds with the creation of locally convectively unstable regions downstream, which encroach onto the locally absolutely unstable region until the local instability is suppressed. That local instabilities exist only if absolutely unstable regions span a minimum size is verified by eigenvalue calculations of three-dimensional flows. Numerical examples suggest that this critical size is at least 9000 km for a wide range of parameter values chosen to investigate the midlatitude storm tracks. Fluctuations arising from local absolute instability obtain maximum amplitude in the downstream convectively unstable regions rather than in the absolutely unstable regions themselves. Together, these results suggest that if an equilibrated absolute instability were to occur in midlatitudes, a zonal band of surface easterlies exceeding 900 km would be required and the associated enhanced variances would not be found coincident with the regions of absolute instability.

Delsole, Timothy M.↗

NASA NTRS1977

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗

NASA NTRS1992

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

Huck, Friedrich O.↗

NASA NTRS1988

Evaluation of a three-dimensional empirically derived wing at supersonic speeds

A novel wing design concept is introduced which takes advantage of the existence of conical flow at supersonic speeds. The present wing design concept is to create a near conical wing geometry by redistributing airfoils in a spanwise direction. In addition, a set of graphs which review the supersonic aerodynamics of delta wings have been employed to select a design wing sweep and Mach number. An iteration through the wing design logic resulted in the selection of a 65 deg swept delta wing and a design Mach number of 1.62. Theoretical analysis was performed with a nonlinear full-potential analysis method to assess the merits of the wing design approach. The analysis showed large reductions in drag due to lift compared to delta wings configured with traditional thickness and airfoil distributions.

Wood, Richard M.↗

NASA NTRS1985

Atmospheric chlorine and stratospheric ozone nonlinearities and trend detection

It is pointed out that at the present time there is no experimental means to detect the current reduction of stratospheric ozone by chlorine from fluorocarbons relative to its unperturbed amount. The reason for this situation is related to the small changes involved and several possible masking effects. As a substitute for experimental detection, there have been many stratospheric modeling efforts. The history of these efforts has been reviewed by Cicerone et al. (1983). Results obtained by Cicerone et al. imply that the successful detection of net ozone destruction by chlorine would be delayed many years from the present time. The present paper is concerned with a reinvestigation of the photochemical problem discussed by Cicerone et al. on the basis of an independent one-dimensional model reported by Herman (1979). It is concluded that by the year 2020 the total ozone decrease due to ClX should be about 3 percent (2.5 percent with increasing methane). Such a change may already pose environmental problems.

Herman, J. R.↗

NASA NTRS1988

Control of the boundary layer separation about an airfoil by active surface heating

Application of active control to separated flow on the RC(6)-08 airfoil at high angle of attack by localized surface heating is numerically simulated by integrating the compressible two-dimensional nonlinear Navier-Stokes equations solver. Active control is simulated by local modification of the temperature boundary condition over a narrow strip on the upper surface of the airfoil. Both mean and perturbed profiles are favorably altered when excited with the same natural frequency of the shear layer by moderate surface heating for both laminar and turbulent separation. The shear layer is found to be very sensitive to localized surface heating in the vicinity of the separation point. The excitation field at the surface sufficiently altered both the local as well as the global circulation to cause a significant increase in lift and reduction in drag.

Maestrello, Lucio↗