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At least 163 records · Page 9

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NASA NTRS1980

Latitude-dependent sensitivity to stationary perturbations in simple climate models

The steady-state zonally averaged climate is perturbed by adding a latitude-dependent heat source to an energy balance equation of the simplified Budyko-Sellers type. The latitude of the ice edge, which is attached to an isotherm, becomes dependent on the strength of the perturbation. This dependence is given in terms of the well-known iceline-solar constant relation, and the latitude dependence of the perturbed temperature field is then uniquely determined. The exact analytical solution is linearized and expressed in terms of a superposition of line sources at various latitudes. The main features are: (1) The total temperature response is a sum of the direct effect of the perturbation and an indirect ice-albedo effect proportional to the solar ice-edge sensitivity; and (2) the indirect feedback effect produces an enhanced response in polar latitudes.

Salmun, H.↗

NASA NTRS1983

Development of a multiple-parameter nonlinear perturbation procedure for transonic turbomachinery flows: Preliminary application to design/optimization problems

An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations.

Stahara, S. S.↗

NASA NTRS1984

Effects of the pressure perturbation field in numerical models of unidirectionally sheared thunderstorm convection - Two versus three dimensions

The physical roles of 'buoyant' and 'dynamic' pressure components, and the distinction between buoyant and hydrostatic pressure perturbations, are aspects of the pressure perturbation field in strongly sheared convective storms studied by means of two- and three-dimensional anelastic numerical modeling experiments with common environmental profiles. The pressure analysis clarifies the differences between two- and three-dimensional storms. In the main updraft, strong midlevel thermal buoyancy is partly opposed by a downward-perturbed vertical pressure gradient force. This, however, occurs to a much greater extent in two dimensions than in three, contributing to smaller net upward accelerations. While the buoyant and hydrostatic fields are intimately related to the total buoyancy distribution, the buoyant pressure perturbation is smoother and of lower amplitude than its hydrostatic counterpart. For the model experiments, this distinction is far greater in three dimensions than in two, in association with the smaller scale of the active convection in three dimensions.

Schlesinger, R. E.↗

NASA NTRS1986

Sensitivity of an atmospheric photochemistry model to chlorine perturbations including consideration of uncertainty propagation

Models of stratospheric photochemistry are generally tested by comparing their predictions for the composition of the present atmosphere with measurements of species concentrations. These models are then used to make predictions of the atmospheric sensitivity to perturbations. Here the problem of the sensitivity of such a model to chlorine perturbations ranging from the present influx of chlorine-containing compounds to several times that influx is addressed. The effects of uncertainties in input parameters, including reaction rate coefficients, cross sections, solar fluxes, and boundary conditions, are evaluated using a Monte Carlo method in which the values of the input parameters are randomly selected. The results are probability distributions for present atmosheric concentrations and for calculated perturbations due to chlorine from fluorocarbons. For more than 300 Monte Carlo runs the calculated ozone perturbation for continued emission of fluorocarbons at today's rates had a mean value of -6.2 percent, with a 1-sigma width of 5.5 percent. Using the same runs but only allowing the cases in which the calculated present atmosphere values of NO, NO2, and ClO at 25 km altitude fell within the range of measurements yielded a mean ozone depletion of -3 percent, with a 1-sigma deviation of 2.2 percent. The model showed a nonlinear behavior as a function of added fluorocarbons. The mean of the Monte Carlo runs was less nonlinear than the model run using mean value of the input parameters.

Stolarski, R. S.↗

NASA NTRS1984

Shuttle derived atmospheric density model. Part 2: STS atmospheric implications for AOTV trajectory analysis, a proposed GRAM perturbation density model

A perturbation model to the Marshall Space Flight Center (MSFC) Global Reference Atmosphere Model (GRAM) was developed for use in the Aeroassist Orbital Transfer Vehicle (AOTV) trajectory and analysis. The model reflects NASA Space Shuttle experience over the first twelve entry flights. The GRAM was selected over the Air Force 1978 Reference Model because of its more general formulation and wider use throughout NASA. The add-on model, a simple scaling with altitude to reflect density structure encountered by the Shuttle Orbiter was selected principally to simplify implementation. Perturbations, by season, can be utilized to minimize the number of required simulations, however, exact Shuttle flight history can be exercised using the same model if desired. Such a perturbation model, though not meteorologically motivated, enables inclusion of High Resolution Accelerometer Package (HiRAP) results in the thermosphere. Provision is made to incorporate differing perturbations during the AOTV entry and exit phases of the aero-asist maneuver to account for trajectory displacement (geographic) along the ground track.

Findlay, J. T.↗

NASA NTRS1988

Investigating a hybrid perturbation-Galerkin technique using computer algebra

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Andersen, Carl M.↗

NASA NTRS1989

A hybrid perturbation-Galerkin method for differential equations containing a parameter

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1989

Linear stable unity-feedback system - Necessary and sufficient conditions for stability under nonlinear plant perturbations

The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to Delta P or not; 2) allowing the observation of the output of Delta P or not. The plant perturbation Delta P is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations Delta P for which the perturbed system remains stable.

Desoer, C. A.↗

NASA NTRS1990

Analysis of wind perturbation activity for the NSTS launches

A method for statistical analysis of wind perturbation activity is proposed for application in NSTS prelaunch assessment of the wind environment. Methods for comparing day-of-launch wind perturbation standard deviations with historical data at the launch site are described. A statistical model based on the Gumbel extreme value distribution is developed for the largest vector and component perturbations in a wind profile as a function of high-pass filter cutoff wavelength. Application of the model is proposed for assessing extreme perturbations within prelaunch sequential Jimsphere wind profiles.

Adelfang, Stanley I.↗

NASA NTRS1990

Cosmic-string-induced hot dark matter perturbations

This paper investigates the evolution of initially relativistic matter, radiation, and baryons around cosmic string seed perturbations. A detailed analysis of the linear evolution of spherical perturbations in a universe is carried out, and this formalism is used to study the evolution of perturbations around a sphere of uniform density and fixed radius, approximating a loop of cosmic string. It was found that, on scales less than a few megaparsec, the results agree with the nonrelativistic calculation of previous authors. On greater scales, there is a deviation approaching a factor of 2-3 in the perturbation mass. It is shown that a scenario with cosmic strings, hot dark matter, and a Hubble constant greater than 75 km/sec per Mpc can generally produce structure on the observed mass scales and at the appropriate time: 1 + z = about 4 for galaxies and 1 + z = about 1.5 for Abell clusters.

Van Dalen, Anthony↗

NASA NTRS1990

Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I - Power-law growth of morphological instabilities. II - Nonlinear development

The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.

Pines, V.↗

NASA NTRS1990

Causal compensated perturbations in cosmology

A theoretical framework is developed to calculate linear perturbations in the gravitational and matter fields which arise causally in response to the presence of stiff matter sources in a FRW cosmology. It is shown that, in order to satisfy energy and momentum conservation, the gravitational fields of the source must be compensated by perturbations in the matter and gravitational fields, and the role of such compensation in containing the initial inhomogeneities in their subsequent evolution is discussed. A complete formal solution is derived in terms of Green functions for the perturbations produced by an arbitrary source in a flat universe containing cold dark matter. Approximate Green function solutions are derived for the late-time density perturbations and late-time gravitational waves in a universe containing a radiation fluid. A cosmological energy-momentum pseudotensor is defined to clarify the nature of energy and momentum conservation in the expanding universe.

Veeraraghavan, Shoba↗

NASA NTRS1991

Remote sensing of mesospheric and thermospheric density perturbations induced by subtropical heavy rainfalls for spacecraft environment study

The simultaneous measurements of VHF radar and HF Doppler array systems are used to observe three-dimensional wind speeds and gravity waves with the purpose of determining the density perturbations at different heights of mesosphere and thermosphere induced by the convective motions associated with subtropical heavy rainfall during the time period of the raining season. Frequency, horizontal wavelength, vertical wavelength, and phase velocity of the gravity waves are determined from the Fourier power spectral analysis of horizontal and vertical wind velocities. The results are compared with those of density perturbations caused by typhoons, tropical storms, and winter-time drizzles associated with convective motions. It is shown that the maximum amplitude of the density perturbations caused by the gravity waves is +/- 10 pct which is greater than that of density perturbations caused by gravity waves associated with weak convective motions in winter time and is smaller than that caused by the gravity waves associated with tropical storms.

Hung, R. J.↗

NASA NTRS1991

Nondimensional forms for singular perturbation analyses of aircraft energy climbs

This paper proposes a systematic approach for identifying the perturbation parameter in singular perturbation analysis of aircraft optimal guidance, and in particular considers a family of problems related to aircraft energy climbs. The approach, which is based on a nondimensionalization of the equations of motion, is used to evaluatae the appropriateness of forced singular perturbation formulations used in the past for transport and fighter aircraft, and to assess the applicability of energy state approximations and singular perturbation analysis for airbreathing transatmospheric vehicles with hypersonic cruise and orbital capabilities.

Calise, A. J.↗

NASA NTRS1991

Propagation of perturbation energy fluxes in the subsolar magnetosheath - AMPTE IRM observations

The propagation properties of perturbation energy fluxes of subsolar magnetosheath fluctuations were studied. The Poynting flux, kinetic energy flux, and enthalpy flux are calculated using magnetic field and plasma measurements from the AMPTE IRM satellite during five intervals in 1984. The results are then compared with a disturbance indicator R of the magnetic field in the same magnetosheath region. It is shown that during disturbed periods with large transverse variations (low R level), the perturbation Poynting flux and the kinetic energy flux increase, and a significant portion of the fluxes consistently propagates toward the magnetopause. The Poynting flux of those fluctuations which consist of mainly compressional perturbations does not appear to propagate in any certain direction. The enthalpy flux of the perturbations does not propagate in any certain direction in any of the cases. The kinetic energy flux appears to be more important in exciting harmonic ULF waves in the dayside magnetosphere.

Lin, N.↗

NASA NTRS1992

Comparison of the Unified Perturbation Method with the two-scale expansion

The Unified Perturbation Method (UPM) converges faster over a wider domain of surface roughness than other perturbations, such as the small perturbation method, the phase perturbation method, the Kirchhoff approximation, and the momentum transfer expansion. It can be shown that UPM intrinsically possess characteristics similar to the two-scale expansion without requiring a free parameter. This paper considers whether the UPM can be improved by applying the two-scale concept to the method. In order to do so, the unknown source current is expanded in a two-scale manner starting from the extinction theorem. Several two-scale expansions are derived and are compared with the conventional two-scale approximation. It is shown that the UPM performs best without two-scale expansions.

Kim, Yunjin↗

NASA NTRS1992

Singularity perturbed zero dynamics of nonlinear systems

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

Isidori, A.↗

NASA NTRS1993

An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals

A new open-shell perturbation theory is formulated in terms of symmetric spin orbitals. Only one set of spatial orbitals is required, thereby reducing the number of independent coefficients in the perturbed wavefunctions. For second order, the computational cost is shown to be similar to a closed-shell calculation. This formalism is therefore more efficient than the recently developed RMP, ROMP or RMP-MBPT theories. The perturbation theory described herein was designed to have a close correspondence with our recently proposed coupled-cluster theory based on symmetric spin orbitals. The first-order wavefunction contains contributions from only doubly excited determinants. Equilibrium structures and vibrational frequencies determined from second-order perturbation theory are presented for OH, NH, CH, 02, NH2 and CH2.

Lee, Timothy J.↗